Twitter's Chrome notifications on Android don't mirrored to desktop by PushBullet

[AC Question]

Hello Forum *,

Environment -
Device: Nexus 5
Android version: 6.0.1
Chrome for Android version: 60.0.3112.107
I use Chrome for Android to access to Twitter.
I have set up Twitter's per-profile-mobile-notifications.
I use PushBullet to mirror this device's Android notifications to my desktop's Chrome PushBullet extension.

Issue -
These Twitter notifications are not mirrored by PushBullet

Remarks -
- All other Android notifications got mirrored perfectly without any problem
- I know how to control PushBullet's per app behavior

My questions -
- Can I get "universal notifications" from Twitter (when a notification comes, it appears on all my devices. And when I open or dismiss on one device, all other devices' notifications are dismissed) without using its app or other third party services?
- If no, how can I get PushBullet mirroring those Twitter's Android notifications?
- Your advices to me?

Please feel free to ask for additional info if it helps to solve my problem.
Thanks and have a good one