[OHBBREF]

I think thatyou will find that NHFS Rule 3 section 3 Article 1 D covers the situation
If entry is at any time other than between quarters, and a substitute who is entitled and ready to enter reports to the scorer, the scorer shall use a sounding device or game horn, if, or as soon as,the ball is dead and the clock is stopped.
and NCAA Rule 3 section 4When entry is any time other than between halves, and a substitute who is entitled and ready to enter reports to the scorer, the timer shall sound the horn when (or as soon as) the ball is dead and time is out.

there is also information about being beconed onto the floor - however the scorer or timer is by rule to sound the horn to notify the officials of a substitute.

Now if you are allowing subs to enter from the bench - because someone is yelling sub then a whistle may be necessary -
IMHO you are wrong - the player should be at the table ready to go at the dead ball to be allowed to enter the game at that time. it is the rule if you enforce it they will adapt.