In MTG I know creatures suffer from "summoning sickness" when first laid unless they have "haste"?

and abilities that have "tap" in there activation cost can't be played until the very start of your next turn unless that creature has haste but does "summoning sickness" even effect an ability like "Rushwood herbalist's" in which the creature's ability states "(pay one green mana),(tap), Discard a card from your hand: Regenerate target creature" the "tap" comes after the mana cost so I wanted to double check even though i'm 99.99% sure the ability is useless until your next turn because "tap" is in its cost. Thanks!