Guess what, my setting has been on silent and it"s not working?! Crap..
I've googled for some days but to my dismay, I couldn't find a workable solution. What that were shared were either outdated (for an older android version) or I"m already on the recommended setting which didn't work for me!
After meddling with my phone again and again, I think I finally found a solution. At least now my twitter notification doesn't come with vibration anymore!
So here's the solution:
1) Go to your phone's Settings > Sound and vibration
2) Go to vibration intensity
3) Under "Notification", set it to the lowest.
Voila!