For the 'Esuna test', I've finished casting mount chocobo while autorun is on, but I do not actually get on the mount even if I finish the spell. This suggests the server decides whether you get on the mount or not, and even if its response is late (or not at all), you still don't get on the mount. Note that this also works in reverse. You can definitely move with about 0.3s left on any spell and it will almost always finish casting. Your client can easily tell you this action is impossible, but it doesn't matter because it's not the one making the decision. As long as the server says it's okay (and it's okay because to the server you never moved, due to lag), it's also okay to the client.