Boss asked me to get to work early but coworker doesn't?

I work overnights starting at midnight and finish at 8am. Recently, my supervisor asked me to arrive to work around 11:45pm instead of my usual 11:55 because sometimes I have been late and wants to make it "nice" but does this really warrant me coming to work 15 minutes early? My job is the kind where you arrive, you relieve the co-worker from their shift so that means the co-worker gets to leave 15 minutes early. On top of that, my co-worker who comes at 8am to relieve me usually arrives past 7:55 or just barely. I honestly do not like "tattling" on my coworkers so what should I do?