This Trap doesn't work the same way as other Traps. Rather than having an optional alternative cost, Stone Idol Trap has a mandatory cost-reduction ability.

An "attacking creature" is one that has been declared as an attacker this combat, or one that was put onto the battlefield attacking this combat. Unless that creature leaves combat, it continues to be an attacking creature through the end of combat step, even if the player it was attacking has left the game, or the planeswalker it was attacking has left combat.

If you cast Stone Idol Trap during your opponent's declare attackers step, the Construct token you put onto the battlefield will be able to block that turn.

The Construct token isn't exiled until the beginning of *your* end step. If you cast Stone Idol Trap during another player's turn, the token remains on the battlefield after that player's turn ends. During your next turn, it will no longer have "summoning sickness" and you'll be able to attack with it. Then, at the beginning of that turn's end step, it'll be exiled.

The cost-reduction ability doesn't care who controls the attacking creatures. If you like, you may cast Stone Idol Trap during your own combat phase, in which case it will count your attacking creatures. If you do, however, the token you put onto the battlefield will be unable to attack that combat and will be exiled later that turn.