I was able to finally get the push notifications work. The steps are below. Mind you I attempted a few things in the previous days prior to these steps. So those few things might help if you are still having problem after applying the fix below. Those few things were: deleting and reinstalling twitter app, restoring the iOS device, revoke and undo revoke all my ios apps in my account settings on twitter's website.
Important: If you have multiple ios devices, make sure you apply these steps to all devices at the same time.
1 Open twitter app
2 go to the profile of each of the people you are following. Click the person icon and select turn off notifications.
3 Go to Me / settings / notifications. Turn off all notifications.
4 Go to your iOS device settings / notifications / twitter. Turn off all notification options.
5 Turn off all your iOS devices. Wait for a few minutes.
6 Turn on the devices. Go to twitter app / me / settings / notifications. Check if all the notifications on all devices are still set to Off. If any option is not showing as Off, set it to Off. Repeat step 5 for all devices. Repeat again if necessary.
7 if all notifications are set to off when you turn the devices back on, you can now turn on your twitter notifications for all devices as usual. Don't forget to visit the notification center.
Hope it works for you.