Talking about warp factors and talking about time dilation don't go well together, unfortunately. The Star Trek universe is, as best I can figure out, nonrelativistic.
This is a bit of hand waving (which is OK because we're talking about imaginary sci-fi constructs) but it was my understanding that since warp drive bends space around you, you're not actually going anywhere near the speed of light, and therefore you experience time similarly relative to people at rest.
