The Jabber Tzeentch's post in Pile in and attack twice was marked as the answer
From what I can see there's two different styles of ability:
A. The ability states you may pile in and attack twice.
B. The ability states you may pile in and attack twice immediately.
Therefore you can assume that any wording that doesn't contain words to the effect of "immediately" means the second pile in and attack happens in usual sequence, allowing an enemy unit to attack.