[OHBBREF]

If the whistles blow at approximately the same time then you have to get together to see which actually occured first.
If the whistle to end the quarter occured first, there would be no shot attempt, if it is a non-shooting foul, (presumeably non bonus also). The ball was dead and unless you feel the need to call the foul, such as excessive contact or something of that nature you might want to back away from it since now it is contact during a dead ball and we have a whole new set of issues to deal with.

The whistle should always be blow to end time in a period. It should be blown by the official whose responsibility it is in the mechanics manual.
The precise reason is is that in section 7 of rule 6 live ball dead ball nowhere does it mention that the horn makes the ball dead.
and in Section 6 of rule 5 scoring and timeing regs, it mentions that the period ends when the signal sounds not that the ball is dead.

The Whistle needs to be sounded to establish a dead ball, with noted exceptions of the rules.