Too slow start up with Atmega2560 on custom PCB
I am closing the case. It is not 100% satisfaction though. Because, using Visual Studio with Visual Micro didn't help me on that issue in a natural way but something else.

For the future reference for somebody might get benefit out of this, I like to explain here what I did to get over this issue briefly. As @Gerben (big credits go to him) has pointed the right direction, I did check fuses by installing Atmel Studio 7 and use its programmer. 

Yes, the fuses were completely wrong. I have therefore read the fuses from my healthy PCB and noted aside and then applied these very same fuse settings to the slow working PCB. I have just programmed the fuses, Firmware was the one I programmed earlier in the uC. So, voilà, the slowness has gone. 

I think I am going to use Atmel Studio 7 now on next to Visual Studio as it has everything built-in including Arduino support. 

Thanks everybody involved.