"Primary" just means it's not in one of the other tabs.
After you've checked the messages you want to move, open the Labels menu. Make sure that the pseudo-labels for the inbox tabs (i.e., "Social", "Promotions", "Updates", "Forums") are not checked and Apply the change. (If some messages are in a label and others aren't there'll be a – in the checkbox. Be sure to clear that.)
If necessary you can use the Move to Inbox button (if available) to make sure the messages are in the Inbox. (You may need to re-select your messages.)
Note that this (probably) won't train Google which messages should be auto-sorted to those tabs. To do that you need to drag-and-drop between the tabs. (A pain in the neck if, like me, you're far from accomplishing "Inbox Zero".)