First, what do you mean by the Roku Remote turning the TV back on? Are you referring to pressing a button on the remote and the TV powers on? That is expected behavior. Just don't press a button on the remote if you don't want the TV on.
Now, if the TV is turning on without touching the Roku remote, then your TV is getting a CEC signal from the Roku (or perhaps something else connected to it). CEC is fantastic when it works as expected, but sometimes it does strange things like this. You can disable CEC on the Roku in the Settings menu, where it's labeled as One-Touch play. In your TV it's labeled as AnyNet+. You might need to disable it in both places. In any event, it's not the Roku remote itself that is doing it.