Not of This World's first ability checks the current state of the targets of the spell or ability it's targeting to determine whether one of them is a permanent you control. For example, say a player casts Forked Bolt targeting you and a creature you control. If, in response, another spell or ability causes that creature to no longer be under your control, then you can't cast Not of This World targeting Forked Bolt. Alternately, if you cast Not of This World targeting Forked Bolt and, in response, another spell or ability causes that creature to no longer be under your control, Not of This World won't resolve when it tries to resolve for having an illegal target.