Waiting to repeat behind the Mo’athin and saying the Duaa afterwards is better! One can pray as soon as he finishes saying the athan!

I grew up seeing people standing when they enter the masjid and the muazzin is saying the athan, they wait till he finishes then they perform the nawafil. I adopted it too, I now thought hey, I have never asked about it & never heard any scholar talks about it. Is this practice Ok? And can someone just perform his nawafil even if the athan is being called?