Eventually over time all traffic will move to the custom domain. It will probably take a month for web earch engines to completely switch to your new site (when they try to re-index your old site the redirect will tell them that it has moved).
In the mean time I think you will have two separate entries in the webmaster tools and need to manually agregate figures, though it won't eb long before you can drop access to the old site as insignificant.
I don't know what you mean by "Do you know how I can check my primary URL in WordPress?". If you want to know which one is selected as a primary it is the one that gets displayed in the URL bar when you browse your site - or you can look at the one selected as "primary" on your domain list in the Dashboard->Store->Domains.