IIRC, George Takei claimed in his autobiography Sulu was XO in TWOK, for whatever that's worth.
The conversation in the travel pod seems clear that he hasn't been on
Enterprise recently, but I suppose XO in addition to helmsman could have been his assignment for the training cruise.
Honestly, the movie is all over the place with regard to what's happening with the TOS crew. At the end of the
Kobayashi Maru test, McCoy (who still seems to be
Enterprise's CMO) has dialog indicateing they're training a new crew specifically for
Enterprise, which rules her out of being a full-time training vessel - and the presence of most of the TOS characters for the
Kobayashi Maru test would imply that they are intended to be part of this new crew, otherwise, why would they even be there? (Although, I suppose they could have partaken in the test to familiarize themselves with Savvik and other cadets as they'd only been temporarily assigned to
Enterprise for the training cruise, but if that's the case, it seems odd that Chekov is the only one that actually had a real job at that moment.) Spock is captain for the training cruise, but his dialog states he is content being a teacher in command of a training cruise, which makes it seem like he's not interested in commanding a future deployment, in which case you'd think
Enterprise's next actual captain should be there.