well, this may sound simple and obvious but try putting this in the trigger
pick all units in UnitGroup[10] and Game display text message (name of picked unit)
before you try to move a random unit
cause you really have to make sure the units are actually in UnitGroup[10], and even if they are in a unitgroup you have to make sure its not like UnitGroup[0]
cause once a unit is in the group it should pose no problem to do any of those
I tried out what you suggested, nothing shows up, so apparently its a problem with the adding to the group, which is odd because its a very simple trigger:
Ladder 10 Enter
Events
Unit - A unit enters RegionB <gen>
Conditions
Actions
Unit Group - Add (Triggering unit) to UnitGroup[10]
Don't see what could really go wrong with it, unless its something screwy with the variable perhaps.
Edit: Seems that it was the variable, the array size was not 10.