If a player Gusts their own unit, must Falling Star or Icathian Rain target friendly units?

When an opponent casts Icathian Rain or Falling Star, you can remove your own units with Gust or Recall before the reflexive triggers resolve. A player asked whether the caster must then choose their own units or whether the spell whiffs.

If a player removes their own units in response to Icathian Rain or Falling Star, must the caster choose their own units for the reflexive triggers?