"one of them had asked my manager to continue..."
You've become aware of this request, but have you asked anyone involved why that special request was made?
One obvious possibility is that your former peer (and now nominal subordinate) is also being groomed for some kind of promotion.
Another explanation is that there is already project work underway on which your manager and your subordinate already share a close understanding and an effective working relationship, and they want to continue that until the conclusion of the project (rather than spending time at a late stage on introducing you as a mediator, when you already have plenty on your plate in a new role).
There are a variety of other possibilities - including personal affinity, or a shared interest in some topic, or even just an indulgence which your manager has granted as a transitional arrangement.
The bottom line is that you need to communicate to get an understanding of what's going on, and provided your manager is not disrupting your ability to coordinate your team and their working time, or riding roughshod over your decisions, then there isn't anything untoward about these meetings.
My suggestion would be to approach your manager with the questions, but don't do it with the preconceived idea that there is something improper going on.
If there is any tenet of "management structure" at all, then your manager has the right in principle to hold meetings with your subordinates.