Time dilation isn't a theory, it's a fact. See http://en.wikipedia.org/wiki/Time_dilation This should have been covered in your high school physics course. IMPORTANT: Time dilation is VERY INTEGRAL to the Gunbuster story.
Lukushiyon was approaching lightspeed, not in warp. They went there to assess survivors and possibility of spaceship retrieval. Unfortunately the bridge was destroyed during it's battle with the aliens. No survivors, no controls, time to get the hell out of there.
They had only 10mins to do their reconnaisance since 10mins relative to them while they approach lightspeed is 6 months for everyone else who are not traveling near light speed.