Hey !

You need to pay the fee once you  have been offered the seat in any of the Institutes.(IIT's, NIT's, IIIT's, GFTI's) . Candidates who participated have registered and locked their choices are allotted seats according to their rank, preferences, category and availability of seats.  The seat acceptance fee in then paid  if you have been allotted a seat and wish to accept it. Candidates will have to  also download JoSAA 2019 provisional seat allotment letter. The acceptance fee is around, 35,000 (General candidates) or Rs. 15,000 (SC/ST/Gen-PwD/OBC-NCL-PwD/SC-PwD or ST-PWD ).You just need to pay the fee once you accept the seat. So according to your query, to be eligible for 2nd round of counselling there is no such requirement.

Do check the below link for more info.

https://engineering.careers360.com/articles/josaa-counselling

Hope this helps

All the best !