You're right in your assumption that it takes place during the movie, but a television tie-in doesn't have to remain faithful to the source material when advertising something else.
Let's take your example of South Park, where they released a tie-in episode for the video game. The episode featured cut content from the game (scenes that were shown at media events such as E3 but were absent from the game and were, instead, added into the episode). It also featured a subplot featuring Mark Zuckerburg acting like a robot, because of that weird interview, that had no actual relation to the video game.
Now, they can't put in cut content from the game into Tangled, because of the radically different art styles, but they could employ other elements to deal with a Kingdom Hearts cross over.
The episode could be set as a flashback to events during the movie (which is always a cheap option that tarnishes the source material). They could have it show some aftermath of Sora, Donald, and Goofy's arrival (subverting having to add in those characters but the other hand means it's not a direct cross over). Or they can say "stuff you" to Nomura and have a plot that doesn't have an actual bearing on Kingdom Hearts 3 at all, and is a fun, non-canonical adventure where Rapunzel teams up with Sora.