Different fish activate different Fish Eye timers. It seems to be random which fish eye timer will activate if there are multiple to choose from (as is the case with Functional Proto-hropkens and Barreleye's fish eyes at the Flagship), but it's not random which timer corresponds with which fish. This guy was probably just repeatedly activating Fish Eyes until he got the timer he knew was for Hropkens. The same thing can be done for Fossiltongues vs Lavalords vs Lord of lords at Halo and Bishopfish vs Priestfish at Clearpool.

Now this is just the way I have been assuming it works as I've caught all these fish, and my experience as well as the comments on ffxivangler support this.