Can you provide a link to where you're reading that?
On the "AAMC Recommendations for Medical School" link (
https://www.aamc.org/students/applying/recommendations/62826/policies_admissionofficers.html), I don't see anything that suggests schools are obligated to make decisions within 2 weeks of the 15th.
The closest thing to that is item #6, which simply says that, after May 15, the school may require applicants to respond to acceptance offers in less than 2 weeks. Even that has nothing to do with May 29th. It just says if an offer is made in mid July, then the school might force the accepted student to make a decision 2 weeks from mid-July. As far as I know, May 31 is all Tufts promised. Could be wrong though.