At the start of each round, it will tell you the type of round. You need it to state Race. You need to get to the finish line 1st and with a little room before anyone else.
I would recommend practicing an emote during a normal round to see it working. Any motion will stop the emote from starting.
You need to stop moving, then press any button on the d-pad to emote. Once it starts, you can run over the line. Running will cancel the emote, but it will still count for the trophy. The trophy will pop once the round ends, not when you qualify.