if it was a minion in your hand, the trap will trigger. if it was a spell, it won't.
pretty straightforward, it depends on what you play
this is the same reason that counterspell doesn't go off on any of the random spells in the brawl - what you played from your hand was a minion, not a spell.
You can play Living Roots all day and Sacred Trial will not trigger. Saplings are summoned, but not played.