If you haven't already gone poking around; Under the Unifi Network controller software on your UDM Pro SE, the WiFI auto-association for UniFi devices can be disabled. Under settings (gear icon under Unifi Network), then System, then the Advanced Tab, then at the bottom "New WiFi Device Auto-Link" and uncheck it to prevent it from automatically associating unifi devices to your wifi network. Now i'm unsure if that disables the hidden SSID for them or not as I haven't checked that via Wireshark, but I just did it for security reasons.
Always interesting to see what's really going on when these things are introduced to a network. It may look like magic to the average punter but it always has to boil down to packets "on the wire", so to speak.