No, that is not true. Counselling with respect to getting seats in an institute when its done online is on the same day for everyone. Then there are various rounds depending upon the exam which allots you institutes based on how many people have accepted the seat. The longer you wait to accept your seat, the better the chances of you getting a seat in a college/branch which you put higher in your preference. I hope this helped, please ask anything else if you have doubts.