The shower drain should be sitting in a slight recess built into the shower pan. The recess allows the shower drain body and strainer to sit essentially flush with the rest of the shower pan floor. Does yours seem to fit that description or not? If it does, then likely the water is pooling up because of residual oils left over from manufacturing and installation. Scrubbing or washing with soap, breaks down the chemicals and allows the water to flow down the drain more easily and stops pooling..
However if the drain appears to be higher than flush with the strainer installed, something else could be going on.
The pan may not be made for the drain installed.
The gaskets meant to be installed below the pan, may have been installed above like a gasket which they're not designed to be.