Twitter notifications not working on iOS6 and Mountain Lion.

I have an iPhone 4, about a month old, updated it 2 days ago to iOS6. Facebook is working, I get my messages and recieve other notifications too, but Twitter is not. No notifications of mentions, retweets, new followers. I believe I've tried everything; re-adding my account, deleting the app, rebooting, checked the settings, - everything's on - I even tried changing my name and adding that!

Weird thing is, that when I go inside the Twitter app on my phone, and try to change the settings, - to get notifications from from "Anyone", instead of just "Follows" - when I quit the app, they all go back to default.

It was working just fine under iOS5, and started doing this about 3 days ago, so that's why I decided to upgrade it.

I also got a new Macbook Pro last week, and immediately updated it to Mountain Lion, I was excited about both Twitter and Facebook integrations. I recieve everything from Facebook here too, but none from Twitter. Did the same thing as on my phone, many-many times, still no luck.

As an alternative option, I set up to get emails, when someone mentions me, I recieve those, but this REALLY annoys me, because Twitter is probably my most used app. It wouldn't even bother me on my Mac, as much as on my phone.

Is anyone experiencing this? I'd appreciate any advice on how to get it working again!