I've been using the label:^smartlabel_group, label:^smartlabel_notification, and label:^smartlabel_promo filters for probably over a couple years now. I have all notifications and promos "skip inbox" and I just go check those labels a couple times a day or when I have a password reset email (which almost always goes to notification). These filters absolutely keep my inbox (which is itself split into 'regular' and 'priority') sane. Having this set up, I don't really see a reason for myself to get the tabbed interface.

Settings -> Configure Inbox -> Save

That turned it on for me.

I also don't have Promotions tab either. I just tried editing Settings and Saving, and still no Promotions tab.

I use lots of filters and labels to categorize my mail already. I have label 'Shopping' and have a bunch of filters set to skip inbox, so I only see it if I click the 'Shopping' label. This works well for sales emails I am subscribed too, but doesn't help for new sales emails, although most of that ends up in the Spam folder.

I believe it was a Gmail Labs feature first, you may have turned it on there.

Google is known for doing partial and test roll outs. E.g. some 5% of users may get a change so they can do metrics on it, then later on they may keep the change and roll it out more or get rid of it.