When are schools generally done accepting students off of their waitlist? Are most done now, or do students still get accepted to schools into the summer?
Contact the schools where you are on the waitlist and ask. Some schools close them around now (they generally do notify people) and others keep them open till school starts. Best to assume you will attending the school you have deposited with.
At some schools, they expect movement through the end of June. Others are done (even if a few accepted students decide to go elsewhere.) If your interest is about a specific school, follow @happy1 's advice.