Dear Dublin, You should wait. However, a good excuse to tell them is the thing you should think about. I also encourage people to apply more as they could, and seriously investigate what potential opportunities these positions could provide. Do not stick on one offer. This should be a "market" which the employers should compete each other, otherwise they will treat poor students very badly.
I also suggest you should have some initial contact with their students (may be visit their lab if possible), and track the publications of these students. You'd better to clarify the following points: (1) How many publications do the students under his/her supervision produced every year; (2) how the supervisor communicate to students, (3) most importantly, do you have any senior team members in the project you involved in your PhD. My experience suggested the supervisor should have a regular face to face contact to student, and it would be good to have a senior member who can provide you experiences in the same research context.
Good luck.