How do I select all emails in on Gmail Category (like the Social tab)?

When you try to select all the items on the first page of the category, it will give you the option to select all conversations.

As you found out you can NOT just do it the "normal way".

You can though by creating a search in the search box.

How to select all emails in a Gmail Category (Social/Promotions/etc tab).

1. Create a search in the search bar: category:promotions

2. Select all by checking the selection box.

(As soon as you check the box you are presented with a message under it, giving you the option to Select all conversations that match this search)

3. Click on the message to select all (and not just the ones on the present page).

You will know that all emails in all pages are selected because you will be presented with the option to clear the selection.

You can read more about "Search operators you can use with Gmail"