Here's a situation: Bob plays a 4 hours Adventurers League Tier 2 adventure with a level 10 character, but due to unforeseen time constraints, the module cannot be completed (only 3 hours in, for example). The end of that module is rescheduled for the following week. In the meanwhile, Bob plays another Tier 2 adventure which gives him enough experience points to go to level 11, therefore being considered a Tier 3 player.
While normally, Bob could not start the first Tier 2 adventure as he has now out-tiered it, can he still join the "wrap-up" session considering he had started the adventure in the right Tier? (in this situation, we assume that Bob refrains from playing Tier 3 adventures until he possibly completes his started Tier 2 adventure)
The AL FAQ says this:
XP is applied immediately upon receiving it, and if it advances you to another level, you do so at the end of the session or the next long rest—whichever happens first. As a general rule, you can’t postpone applying in order to participate in a later adventure. Once you hit the threshold needed to advance to 5th level, for example, that character is no longer able to participate in level 1-4 adventures.
However, I think that the word participate here refers to starting an adventure, not finishing an already started one. Perhaps I missed another relevant section of the FAQ and/or Player/DM guide...
Similar situation to the above example: the experience points gotten before the module is stopped (to be completed the following week) would put Bob to the next Tier.
Other similar situation: Bob would do a long rest during the adventure, getting the XP from the monsters he defeated during the adventure before the rest, therefore advancing to the next level as per the FAQ.