"Classic Baz Style," Pope says. "He was like, 'you're gonna skipper this week - all good?' And I was like, 'absolutely, I'm looking forward to it'."
There are two things at play here. The first is that McCullum and Stokes want to challenge players to take on more responsibility and grow as voices in the dressing room. The second is Pope, beyond being an immensely talented batter, is identified as someone who can be coaxed a little more out of his shell for the benefit of himself and those around him.
That Pope called up Stokes after his appointment as Test captain, and more or less demanded to bat at No.3, rather changed the perception of a boyish scamp who can't help but have a go at anything outside off stump. And the management clearly believe there is more of this type of character within him. Putting him out of his comfort zone - he had only captained once before in professional cricket back in September 2021, for Surrey in a County Championship match against Glamorgan - was clearly their way of bringing it to the fore.
Pope's first day as deputy was spent largely at the crease, flaying the Lions for 146 as England posted 501 for 7 declared. Day two was one of chasing leather as the Lions kept their senior counterparts in the dirt with 411 for 9. Alas, there was no third day in the gig as England opted for a two-hour training session instead. So, how did he find it?
"I enjoyed it actually," Pope says. "I was curious as to what it would be like captaining someone like Jimmy [James Anderson] but I actually really enjoyed it. I wasn't sure whether he'd want to set the field his own way but it was good and we bounced off ideas.
"It was a pretty flat wicket so, on a pitch like that, it makes it a bit more difficult rather than Jimmy just getting four slips and he's just going to nick everyone off. You had to find different ways to get batters out and it was good trying to be creative like that, but I enjoyed it and all the boys were top draw and brought into it."
Pope cedes he'd never really considered captaincy. Beyond doing the job for Cranleigh School and Surrey Under-17s, it was not something he coveted. The FEC (Future England Captain) tag was loosely affixed to him early in his career, simply because of his undoubted ability that saw him win the first of 30 caps against India in the 2018 summer, aged just 20.
Four years on, and heading into a historic tour of Pakistan, he is a little bolder when addressing leadership - both in the long-term future for England, but also when it comes to tactical collaboration within the current team, on and off the field.
"I don't go 'oh I'd love to be England captain', but at the same time I believe I've got a good cricket brain. I think about cricket a lot and I think I see the game in a way where I don't just think about my batting. Whether that be for Surrey or whoever, if an opportunity arose, it's something I'd definitely be keen to do.
"I mean, obviously, we've got the best captain in the world at the minute. Everyone's loving playing under Stokesy but if it was something that happened in the near future, amazing. Something that I'd love but at the same time I realise I've got to score my runs. I don't want to be looking too far ahead about that stuff. I want to keep concentrating on the No.3 spot. It's also something that takes your mind off batting, so I enjoy thinking about the game like that. With Stokesy, there's a lot of boys who bounce ideas while he's skippering as well."
"No, I'm sure there'll be a time if they ever want to announce someone, then they will, but it's nothing like that," Pope says. "I think everyone at the minute has as much say and, if there's a conversation to be had and you want to give your ideas, then great, but there's no tag on it. The natural leaders and the guys in the team who have got something to say will usually say something but, at the minute, it's pretty much a level playing field on that front."
Shedding the "wunderkind" tag is still a work in progress for Pope. Beyond adopting a "grown-up" position at first drop, the raw numbers still need to develop. His career average is 31, and there are just two centuries to his name, the second coming this summer as his first in home conditions. He does, however, feel that little bit more mature, and that little bit more self-assured, thanks to a close-knit England environment that encourages individual growth.
"I felt it a little bit in the summer," he says of being regarded as a senior member of the group. "Playing at three for England in Test cricket is a big role to have and it's an important role for the team. As soon as I was given that role, I saw myself as a bit more of a leader than when I was batting at six, which I really enjoyed.
"It's nothing that's necessarily changed. I think it's the way everyone's feeling in the team at the moment. We're feeling like it's our team in a way, rather than boys feeling like they're playing for their places. It's more like 'this is us, this our team, we can own it, we can dictate how we want to play' and I think everyone's probably feeling an aspect of that as well, which is great for the whole squad and the management as well."
Pope's record last summer was solid: 456 runs at 38, with four fifty-plus scores. Perhaps most encouraging was the manner in which he overcame a poor start - 7 and 10 in the first Test against New Zealand - to make 145 in the next innings against the same opponents at Trent Bridge. His credentials at No.3 were questioned but he approached the issue with far more positivity than he usually would, seemingly deciding on a whim to worry less about a couple of low scores and more expressive. With distance, now, he reflects on the season with more clarity.
"I was very happy with how the summer went, [but] it wasn't necessarily the numbers,' he says. "I averaged 38. That's not amazing but at the same time I was happy with my contributions and on tougher wickets, finding different ways to negotiate bowler friendly conditions, which is what I was happy with.
"Rather than scoring runs when everyone else is scoring runs, score runs when you can stand up and lead the innings," he adds. "It might not be a 100, but even if it's a 70 or an 80 or an 60, that's probably what I was most pleased with from the summer. Hopefully the hundreds will come on better wickets, where I can maybe play a bit more conventionally, but I'm happy with how I went about this summer and I learnt some good lessons as well.
"I learnt that you don't need to hit a million balls a day in practice, and you don't need to overtrain to find success. It's about being full of energy and being confident on the day and almost trying to enjoy the week a bit more, rather than thinking 'oh I need a score'. But there's always room for improvement. If you turn those 5s into 30s and those 70s into 100s, then that's the way you're having an amazing summer, rather than a good summer."
Maturity will come in handy over the next month. Not just because of the challenges that Pakistan offer on the field, but with a return to constricted living day-to-day because of the level of security in place. Pope was open about the challenges of similar restrictions during the 2020 summer, with bio-secure bubbles during the height of the Covid-19 pandemic and how the lack of escape meant "you think about your failures a little more than normal".
"I was pretty new to international cricket at that point and my mood pretty much was dependant on how many runs I scored that day, rather than being at peace," he says. "Not just watching a screen and playing Call of Duty but finding other ways to take your mind away from cricket and just enjoying each other's company more."
More time together as a group, looking out for each other and focussing on three back-to-back Tests will ease that strain, somewhat. Pope, by all accounts, is wiser and more at ease about what is to come.
"The boys are buzzing for it and I can't wait to see the crowds out there," he says. "Even with the levels of security, it's going to be fingers crossed, a smooth operation. It'll be great to be a part of and great to experience as a player, being the first English Test team to tour there in a long time. So we're buzzing for that but it's going to provide its challenges and we probably won't be allowed out of our hotel much. We'll find ways, whether that's card games ... I think Keats has got his coffee machine, so just doing small things like that.
"The fact that we've had a bit of time in Abu Dhabi, we've been able to get out on the golf course and do a lot of training and have our warm-up game has been good, and once we're out there, we're pretty much straight into it. There's not going to be too much downtime anyway."
Vithushan Ehantharajah is an associate editor at ESPNcricinfo