The yu gi oh trap card enlightenment.................…

I used the trap card "enlightenment" ***You cannot Summon the turn you activate this card. Activate at the end of the Damage Step, if a Spellcaster-Type monster you control attacked and destroyed an opponent's monster by battle. That monster can attack again (immediately).*** On my friends pyramid turtle which allows him to special summon another zombie, it was the only card on his field, so my question is did that allow for me to have a direct attack (BECAUSE OF THE IMMEDIATELY PART) or did I have to wait until his special summoned monster got onto the field?