For Ultima, both Ultima and the summoner have to be at critical health. First off, it's pretty hard to even damage Ultima, if you actually run into something that can, chances are neither her or her summoner are going to live long enough to cast it...

The others...

Exodus: Cast Immobolize on him when there is only 10 seconds (one orb) left in his timer.

Zalera: Opponent must have 30% left of his health.

Hashmal: Summoner must be in critical condition.

Zodiark: Summoner must have stone effect on them.

The rest will atuomatically use their Summon attacks when the timer is close to 10 seconds or their health is low...