When an effect lets a Spirit play a Power Card outside of the Spirit Phase, does the Spirit immediately resolve that Power?

When an effect lets a Spirit play a Power Card outside of the Spirit Phase, does the Spirit immediately resolve that Power?

No, except in the rare case where the effect explicitly says the Spirit also gets to resolve the Power in addition to playing it (e.g. the "Ethereal Conjunction" Event). The vast majority of the time, the new Power Card works like any other: resolvable in the Phase in its "Speed" box when not in the middle of anything else.