Yes you should put a tarp under your tent.
When putting up a tent you should always lay an extra tarp under the tent so that the tent doesn't sit on the ground itself directly.
When you do put a tarp under your tent you protect the bottom of the tent and the tent will last longer.
The tarp under the tent will also help prevent moisture from the ground from getting into the tent as easy as it would without it.
You don't have to put a tarp under your tent when putting it up but having a tarp under the tent is the best thing to do.
If you have the tent put up on a beach you should put the tarp inside the tent and not under it though.
But camping anywhere else you should place the tarp under your tent.