What should I do if funding announcements aren't made until after the acceptance deadline?
(Converting my comment to an answer, as suggested by @jakebeal.) Making admission offers without funding is a surprising, and not good, practice on their part, if it is as you describe, since people should make decisions based substantially on funding, not just admission. 

If you have other plausible choices with funding, I'd take one of them. Don't go to math grad school without funding (and tuition remission).

(Unlike possible funding ambiguities, in mathematics, the funding is generally almost entirely by Teach Assitantships, and it should be possible to make (approximate) decisions about how many to fund well before the April 15 U.S. nation-wide decision date. That is, except for some (hopefully anomalous) budget crises, math depts themselves would not be "waiting" to find out funding for grad students.)

That is, this sort of "admission" is possibly a very low bar. Funding is the serious issue. In particular, don't get your hopes up, I'm afraid.