If they are completely done with no other places to be promoted or demoted that has more than one series left in the playoffs, I'd just wait until just before the WS or just after game 1 of the WS. The reason for waiting is because if they just got a promotion cycle or a regular development cycle, a promotion cycle might not occur if you promote too early.
As an examale, if your AA team misses the playoffs, you promote your AA players to AAA. If your AAA team made the playoffs, you leave your AA players in AAA with the hopes that that team advances further in the playoffs. If they lose the first AAA series, you have two choices, you can promote them to the mlb and immediately demote them to HiA assuming your HiA team is still alive. They likely won't get an immediate promotion cycle because you just promoted them to AAA, but by promoting them to mlb, you avoid a demotion penalty down to HiA. The other choice is to just hold them there in AAA until the mlb WS gets closer and enough time has gone by that those 3 to 5 games actually get you promotion bump. It is unlikely they'll get a bump, but it's still a choice. Also, note that, because you're promoting them to mlb, they'll get put on the 40 man roster so you need to be careful with your decisions.