This is a tricky situation. The college won't take your oral acceptance as seriously as a written acceptance, but they may still take it seriously enough to screw things up for them and/or other candidates. For example, their second favorite candidate may be sitting on another offer while waiting to hear from this college. Your oral acceptance may lead them to tell this candidate that it's not worth really pushing to extend the deadline for the other offer.
For this reason, you shouldn't accept an offer, even just orally, unless you are really certain and committed. It's also not in your own interests to accept before all possible negotiations are finished, since your bargaining power decreases dramatically upon acceptance.
Given that you already accepted over the phone, the big question is how seriously they took it. If you had an elaborate discussion premised on the fact that you are joining them next year, then you really need to deal with this if you intend to keep interviewing elsewhere. For example, you could write something like "Thank you again for the offer, which I'm very excited by. I'm afraid that in my enthusiasm, I let the discussion of joining you next year get a little bit ahead of itself, and of course I'll have to discuss the details of the written offer with you before I officially reply." This is definitely awkward, but I don't think there's any non-awkward way of essentially retracting an oral acceptance. (Especially because you don't want to retract it so thoroughly that they lose interest and withdraw the offer.)
If your oral acceptance was more of a passing comment, without any involved discussion or evidence that they took it seriously, then it's a little less awkward. You could just write "Thank you again for the offer, which I'm very excited by. I'm looking forward to receiving the details. What is the deadline for my decision?" That would make it clear that you didn't consider the phone conversation a real decision. But this approach doesn't even acknowledge that your oral acceptance could be an issue, which is really awkward if they did take it seriously, so you should be careful.
Either way, clarity and honesty are the key principles. You don't want them to be taken aback or feel used if you keep interviewing or accept another offer instead.
Wait till I get a formal offer letter from the first campus and then let them know I need more time?
I'd recommend letting them know earlier than that, to minimize the chances that they will make any decisions based on your oral acceptance.
There's a risk that they could be offended and call the whole thing off, but I think this risk should be small if you handle it smoothly, and they could withdraw a written offer too (so getting it in writing won't protect you).