After you pay the cost one or more times, a second ability triggers. Players may respond to the new ability at that point. As that ability resolves, Tainted Adversary gets its counters and the tokens are created.

Decayed represents a static ability and a triggered ability. "Decayed" means "This creature can't block" and "When this creature attacks, sacrifice it at end of combat."

Once a creature with decayed attacks, it will be sacrificed at end of combat, even if it no longer has decayed at that time.

Decayed does not create any attacking requirements. You may choose not to attack with a creature that has decayed.

Decayed does not grant haste. Creatures with decayed that enter the battlefield during your turn may not attack until your next turn.