You can get your Core emails delivered to the Gmail Primary tab instead of the Promotions tab by following the steps below:
Moving emails to the Primary tab
You can move your emails to the Primary tab by clicking and dragging one of the Core emails from the Promotions tab to the Primary tab. By doing so, all future Core emails will be delivered to the Primary tab.
Disabling Promotions tab
Click the Settings icon and then select See all Settings. Click the Inbox tab. Then, uncheck the box next to Promotions and any other unwanted tabs to remove them from the inbox. Click Save Changes at the bottom of the screen. This should hopefully resolve the issue.