Choosing the Best School

So I emailed the graduate director to find out what exactly that statement in the acceptance letter meant and if “successful” students usually continue to get funding. I was directed to the “Joining a Research Group” section of their website here: http://www.ams.sunys…e/phdrequ.shtml. From what I understand, as long as you are academically succeeding and join a research group (get an advisor) within the first year, most students get funding through an RAship. However, the wording of the section seems confusing and not very straight to the point. Does anyone have any knowledge of a similar situation such as this and if I am understanding this right as far as future funding goes?

Thank you very much!