I don't know if there are rules about which preposition to use, but this is how I use them:
Jump upon something means the same thing as jump on something, that is, you are already on the thing and then you jump up and down on it.
If you start on the floor and then jump and land on a thing, then you jump up on the thing. "I can jump up on (or onto) that table."
Upon and Up on may look very similar, but they are pronounced differently and are used in different ways.