When you have Gmail accounts, all your mail is stored in the Gmail “All Mail” Archive folder. You then access that via the various Gmail labels (folders) on the left like in Gmail online.
So if you are using the new V10, unless you changed the default setup, you probably have the default Gmail Categories Tabs enabled where you then “are just not seeing your new mail in your Primary Inbox” and then only show in All Mail unless you clicked the other Category Tabs.