As long as a creature type has the word "Spirit" in it, it will still work. Unless otherwise stated, it doesn't matter if it has (or doesn't have) other types, so long as it has the type mentioned in the card. For example, if I had a card that made all "Soldiers" I control one mana cheaper, and then played a "Kithkin Soldier" type creature, it would still get the -1 mana cost bonus because it's still has the word "Soldier" in its type. Hope that helps ;)
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