Substitute player for the foul shooter

[johnyd]

Please refresh my feeble mind before the season starts. Team A is on the foul line, shooting 1 and 1 or shooting 2. Kid makes both free throws.
Coach "A" sends a kid to the table, who he wants to go in for the shooter. After 2nd made basket, team B quickly grabs the ball and throws it in bounds.
Is it my responsibiity, as trail to see that player, whistle to stop play, after the made basket and allow the substitute to enter?
Should the table blow the horn to get my attention, to allow the kid to come in? Or Is it the coaches responsibility to tell alert me that the player is coming in for the shooter?

Finally, why do we stop play when after Team "A" makes both baskets, they are technically not in posession of the ball, it goes to team B for the throw in. Why do we stop there inbounds effort to even allow for the substitution?