Zoho Desk iOS App | No push notification sent when a ticket is moved to another department

Hello folks,

Our situation is this:

3 departments configured for our Zoho Desk instance.
One department (Technical Support) is configured as the primary (is the only one available for Help Center ticket submissions).
The other two departments ("Developers", and "<redacted> Account Creation") are set to private and can only receive tickets when the primary department manually moves the ticket to them.

This is by design because we do not want regular users choosing which department to submit tickets to. Technical Support will make the determination if those departments should be involved or not.

We have discovered an issue where the mobile app (lock screen on iPad and iPhone) will not receive a push notification for any of the private departments, when a ticket is moved to their queue. This occurs regardless of whether a ticket is moved to them upon arrival (with no updates), or moved to them after it has been replied to etc.

We noticed that the mobile app (by default) has push notifications turned off for all departments, so we turned them on. The problem is, the only push notification available to turn on is for "New Ticket Notifications". There are no other type of notifications that can be enabled, and there are no settings in the web portal management interface that control this behavior for mobile app users (that I can see anyway).

We set one of the private departments to be available on the Help Center briefly, so we could specifically direct a new test ticket to it. As soon as the ticket was submitted, we switched the department back to private. When the ticket arrived directly in to that department's queue, the iOS app push notification worked fine (highlighted in green).

So I guess my questions are:

Is a ticket only classified as "New" when it arrives directly from the Help Center Ticket Form?
Can a ticket be also classified as "New" when it is moved from one department to another?
Is there a way to enable app push notifications to fire when tickets are moved to a department?
In the web portal settings, under Automation > Notify, I only see configuration options for Email and SMS. Are there settings for the mobile app somewhere in there?

It seems a bit odd that push notifications wouldn't be available for anything beyond a new ticket in a help desk app.

Cheers,

Ben