Connect has 3 types of conversations: 1-on-1's, Rooms, and Group Conversations. The rules for are different for displaying notifications for each conversation type.
Connect mobile clients have an APP-level preference that enables/disables message previews on the lock screen. This preference is enabled by default (which means that the contents of the message will be visible on the notification itself). But this can be disabled, and the notification displays placeholder text (like "Greg mentioned you in Rebel Alliance").
1-on-1 and Group Conversations are straight forward. The notifications should always be displayed to the user, and the "is Connecting with you" style text always remains the same for each conversation type.
Note: if notification previews are enabled, then the notification should display the contents of the message.