I would say it is not an oxymoron.
The world did not begin with all current traditions already started. Thus, when something that was NOT a tradition BECOMES a tradition, it is new.
Further, the word tradition implies, but does not require a long-standing history. It might not be much of a tradition, but by definition one could at least argue that merely repeating something a 2nd time qualifies as a tradition -- especially if there is intent to regularly repeat. Traditions have a sense of "weight" or "strength" -- the longer one has been around the more "weighty" or the "stronger" it is. Just because a tradition is very "weak"; or very "new"; doesn't mean it isn't a tradition.
Finally, from a different perspective, the phrase "new tradition" is typically (but not exclusively) used to mean "start something new and hope it becomes a long-standing tradition". From this perspective I would say that "new tradition" is a phrase that means something different from the words that make it up (which is not an oxymoron). I feel like there should be a term for this (maybe generically "trope"), but I can't find it. "Muscle memory" is another example. Muscles do no have memory. The phrase is nonsensical from a strict definition standpoint. But the phrase as a whole has an understood meaning.
