I think what he's saying is that it doesn't kick in the round that it's applied. Though... not sure that's accurate, pretty sure you can paralyze the second fastest person in a 2v2 patch and watch him go dead last instead.
You can paralyze the second fastest person in a 2v2 patch and he'll act second on the turn he's paralysed and thereafter last. Same with Scary Face etcetera, unless someone has a compelling argument on how the hell a Ponyta can outspeed both a Gastrodon and Kirlia while paralyzed for one turn and then never again thereafter.
Might just be that Pokemon decides turnorder at the start of each round, but, it's at least something to keep in mind re: Mewtwo speed arguments. Until its turn comes up it doesn't care about Paralysis.