We had a similar challenge. When we reassigned a record, we needed to have the new owner receive an email notification AND and mobile notification on their phone (near instantly).
Our solution was a Trigger/Flow which would create a Chatter Post on the record on behalf of the user that changed owner, like:
@[userName], this lead has just been assigned ...
This is a known issue https://success.salesforce.com/issues_view?id=a1p300000008XZoAAM
Task reminders are now available to partner users in communities. This
includes users with a partner portal or Partner Community license.
Partner users in communities can see their reminders by clicking Your
Name | My Settings | Reminders
You could do this with a Home Page Component (narrow) and the Streaming API.
Your PushTopic.query would look something like:
'SELECT Id FROM Task WHERE OwnerId = \'' + UserInfo.getUserId() + '\''
Not sure if you want a different lookup field but that's the idea. Whenever your listener picks up an insert, you can kick off whatever popup you want.
The Enable Salesforce Notification Banner is a Global banner (rectangle) that shows in all pages that usually displays Salesforce communications.
What you are looking for is the App Notifications: https://developer.salesforce.com/docs/atlas.en-us.salesforce1appadmin.meta/salesforce1appadmin/s1_admin_guide_notifications.htm
Setup --> Apps --> Mobile Apps -...
This is how the standard functionality works with notifications and the bell.
You'd be better off using some sort of "Today's Tasks" component on a home page than relying on the bell.
You'll need a custom login page for your community. That should allow you to react as soon as a user has authenticated.
Redirect users to a custom auth-page
Setting up a custom auth-page
Once you accomplish the above, your method that returns a page reference should return a page inside your community (success) or an error page/null (failure). If the page ...
In order to disable the email notification on Task creation/assignment, we need to do:
From your personal settings, enter Activity Reminders in the Quick
Find box, then select Activity Reminders.
Deselect Email me when someone assigns me a task.
As you mentioned that you have already done the same, but still getting the mails, I would suggest you check ...