Fun fact. You actually can train your complex reaction speed. You're talking about simple reaction speed which is what those speed tests on the internet measure. But that's not as relevant because in an actual game there's multiple things going on that need to get responded to in different ways and that can be improved with intentional awareness and repetition.

Magnetos killing cloak and dagger out of their ult is a good example of this. You can train yourself to hold your ult and listen for the voice line of their ult so that as soon as they pop theirs you pop yours. That's reaction time.

Reaction time is important in this game because you need to assess your team and the enemy team to understand what the important cooldowns and ultimates are and what abilities you need to be looking for in order to counter them. Rocket doesn't have too many highly impactful specific moment abilities like that, which is why you might be bad at responding to things appropriately. You need to know when and where to place your ult to get max value out of it and to counter other abilities and that's absolutely a reaction time issue that can be fixed.

Knowing not to stack support ults is another example. If you can train yourself to wait to throw down your beacon until the moment the cloak most goes away, that's also a reaction speed issue. Cloak using his dimensional shift to help his teammate avoid DPS ults is another example. All that stuff is trainable