Do we need to cast Spawnsire of Ulamog for infinite spawn tokens?

Annihilator 1 (Whenever this creature attacks, defending player sacrifices a permanent of their choice.) : Create two 0/1 colorless Eldrazi Spawn creature tokens. They have "Sacrifice this token: Add ." : Cast any number of Eldrazi spells from among cards you own outside the game without paying their mana costs.

Activated abilities of creatures you control cost less to activate. This effect can't reduce the mana in that cost to less than one mana.