I curse the twins experiment for the amount of confusion it's caused with relativity. :bitch:
Twins works in general
relativity, because acceleration is absolute. However, in special relativity which is what [B]newtype[b] is discussing, each twin sees themselves aging at the normal rate, and their other twin as aging slowly. Special Relativity involves two objects moving in completely different frames of reference that never meet - ie they don't accelerate. In General Relativity, the frames of reference meet, which causes it to be a lot more complicated, so that's where the Twin thought experiment comes into play.
Not that any of this applies to a warp drive because the ship isn't accelerating, decelerating, or moving. The spacetime around it is, and that's a separate kettle of fish entirely.