The warp drive was used just for fun so we can get to Cygnus X-1 with Warp 1 clocks still synchronized with the inertial frame of ISS.
The wristwatch time lapse for the ISS and Warp 1 are definitely different. The definition of the invariant interval for time is: Wristwatch time t tells the observer in any frame what the time lapse will be on a wristwatch that moves uniformly from one event to the other. In my example (or any relativistic example) we can choose t or t for either frame because they both record the elapsed wristwatch time. We choose dt to be the elapsed wristwatch time, on the ISS, between the event of Warp 1 leaving and then returning and dt for the elapsed wristwatch time, on Warp 1, between the events Warp 1 leaving and then returning. Or vice versa.