Prasanta,

First of all congratulations on being accepted for PhD program at two universities. When it comes to graduate school funding, there is nothing like "one size fits all" notion. The funding criteria and procedure differs from university to university, and even from department to department within a university. For example, few universities only provide instate tuition (as Gohtalo mentioned) where as you qualify for full tuition waiver in other universities with GA/TA/RA.

In your case, I would suggest you to write to the professors who work in the area(s) that you are interested to work on. Tell them you have been accepted to the program and relate your past research/work experience with their research projects. Professors can get their research project funded any time of the year and then they need students to work for them. If you want to take a chance, you can always fund your studies for a semester and look for an assistantship once you land in a school. Your chance of getting assistantship solely depends on you in that case (you have to get a good grade and keep a good rapport with faculty members you are interested to work with).    
Good luck!