The app is most likely using multicast to perform discovery and initial connection to the printer.
As @ww mentioned, bonjour forwarding can be used to send multicast across VLANs (although in my experience it's not always quick/reliable).
Opening a support case and using packet captures is probably the best way to confirm.
If VLAN segmentation between clients and the printer is required, you might be better off either:
- Pointing the clients directly to the printer (if it's just a single printer)
- Setting up a print server to manage the printers, and pointing the clients to that (if you have multiple printers)