Push notifications are still coming after logging out my account.

That is how push notifications are meant to work. They are sent even if the site is not open, as long as you authorise them. Same for all major networks. 

Notifications that you receive while logged-in are the on-site notification alerts. 

Authentication session and notifications authorisation are unrelated. To stop notifications, just turn them off in settings here - https://una.io/page/notifications-settings