I think that "on time" has a linguistic flexibility of meaning similar to "Finished", as in "the job is finished" or '"tomorrow for sure".
There is also a self-sustaining paradox in the timing of events as in:-
"Let's get there on time for once!".
"What for? -We will be the only ones there."
There is also a self-sustaining paradox in the timing of events as in:-
"Let's get there on time for once!".
"What for? -We will be the only ones there."