Generally more than one rounds will be counducted for the counselling for most of the exams as there will be seats left after the first round of the admission. So in order to fill those seats multiple rounds of the counselling or choice filling are counducted by the authority. For AIIMS also there are more than one rounds of the counselling process have been conducted for the filling of the vacant seats. Go through the link to know more about the AIIMS counselling and admissions.

https://medicine.careers360.com/articles/aiims-mbbs-counselling

Dear Sir / Ma'm, if all the seats are filled up by the end of the first round of counselling itself, then it is pointless to conduct the second round. However, it depends on year to year what will be done. Generally second rounf of counselling is done too, only if all the seats are not filled by the end of first round.