So the "on your turn" portion is that not a limit to the effect of fleeing? Really looks like they added that for a reason.
If you were limited when it were not your turn then it would have said "until fleeing ends", or "until you are no longer fleeing".
The question is related to the part of the statement "on your turn"
As for Balance, how is it unbalanced reactions are not very powerful. So I am totally fine with enemies using their reactions while fleeing.