I am recommended to use some insulator or paper sheets when testing PCBs on antistatic mat connected to ground via antistatic wrist band. Is this correct way. Why is it necessary to have insulator sheets in between?
A decent quality rubber antistatic mat will have a low end top surface conductivity of \$ 10M \Omega \$. Working with an audio circuit where the highest impedance is a \$100k\Omega\$? You'll never have a problem. Working with a \$10M\Omega\$ pH sensor? Leakage will cause you problems. This is a question that needs to be answered on a project by project basis, based off the circuit and antistatic mat.
You're betting the bank on the mat having a sufficiently low conductivity that the operation of your circuit won't be affected. This might be the case, but you better had measurements and a rationale from the circuit's design to prove to yourself that it's even supposed to work at all.
So, is it necessary? Only you know the answer. We can't tell you without having a sample of the mat, the schematic of the circuit, and the PCB layout.