When exactly does an attacking creature become tapped?
The attacker becomes tapped during the Declare Attackers step.  The steps of combat are:


Beginning of Combat
Declare Attackers
Declare Blockers
Damage Resolution
End of Combat


So, since the attacker becomes tapped during step 2, it is destroyed before step 4 where it would normally deal damage. 

For a full breakdown of a turn, see this post