The Chronicle X rulebook uses the term "Round" is two different, but similar ways: to refer to a sequence of phases that play out in order, and where the sequence is repeated as part of gameplay. The two different kind of Rounds are:
Turn
A Turn is a sequence of Activations made by the side whose Turn it is, either the Hero Players (collectively), or the Overmind Player. During a Turn, special abilities may trigger or be used which may allow the other side to make an out-of-turn Action or Activation of a Model/Unit, but that doesn't change whose Turn it is.
In particular, the Overmind Player has an ability that once during the Hero Players's Turn allows the Overmind Player to discard two Mutation Cards immediately before a Hero's Activation, and Activate one Alien Unit first.
Note: the rulebook and some card texts sometimes uses the word "Turn" a bit loosely to also refer to the Activation of a a single Hero or Alien Unit.
During the Hero Players's Turn, all the Hero Players activate their Heroes on at a time, in any order they choose.