How should i handle when i encounter an exploiter?

I have a game and i found someone running one of my remote events, so i patched it up and then permabanned the player.

When someone joins it checks if his name is that players, and if it is it kicks him. This is the only way i could think to do this.

I just recently encountered another player who was speed hacking.

SO, my question is... If they player is speed hacking, is it likely that he is also trying to exploit my other remote events and such? Should i permaban speed hackers or just kick them temporarily?

I, if I were you, would just perma ban them and immediately fix the remote event exploit, and possibly add an in-game ban system, as talking to them won't do much, as that's just feeding the fire.