Guiding Spirit is supposed to be exiled when it is defeated, but Tommy’s ability says “reaction: when an asset you control is defeated: gain X resources, where X is the total amount of damage and horror on that asset. Shuffle that asset into your deck.”
Does Tommy’s ability override the card’s Exile text?

No. The Forced effect on Guiding Spirit has been errata'd to be "when" timing rather than "after" timing, and as such, it will take precedence over Tommy's ability (Forced effects with the same timing point as Response effects happen first).

So, by the time Tommy's ability would trigger, the card has already been Exiled and therefore removed from the game.