Dancers and AI...

I can't recall seeing any dancers in Tempest Trials.

I'm not 100% sure on what the AI does but I just bate them and make sure that I stay mindful of rally units. For example, say the AI has young Tiki and Azura and you have Hector and Linde. Tiki is trapped behind some trees so she can't reach Hector to 1hko him, but Azura can. Azura will be bated to attack Hector which is a bad decision for her, but first it will check if Tiki has any rally skills. If she doesn't, Azura attacks and dies. If she does, Tiki rallies Azura but then Azura realizes that Tiki is now in range to attack Hector so she dances and Tiki can now 1hko Hector.

All of the dancers are in the Tempest Trials. Usually the AI will always prioritize an attack over using a support ability ( that being said i have encountered a few instances in which it didn't). The AI will typically favor using Dance/Sing on another unit if:
A. That unit can reach attack range with the aid of a second movement and the Dancer itself is not in range to initiate an attack of its own
B. There is no other unit in range to attack and there is another ally unit in range even though that unit will not enter into attack range.