Your explanation of what is the fix is wrong. Although the easiest way to operate your HomePod is to let it be on the same WiFi. The frequency the WiFi is on nor the network the HomePod is on has nothing to do with operation/functionality of the HomePod.
For a simple setup:
Your phone and your HomePod should be on the same network. WiFi has nothing to do with it. WiFi is just the transport. Following the simple setup process will end up with your HomePod and your phone being on the same network and the same Wifi SSID.
For an advanced setup:
There is no link for advanced setup since Apple only recommends the simple method.
Requirements: I use the below method in my home. It allows for securing your IOT network without putting your users on the same network as your IOT. Your user devices will talk to the hubs on your IOT network and your hubs will talk to your IOT devices.
- Allow mDNS UDP port 5353 destination 126.96.36.199 between the IOT network and the user network
- Put your phone on the WiFi SSID(IOT) that will connect you to the network you want your HomePod to be on.
- Perform the simple setup steps from this link https://support.apple.com/en-us/HT208241
- On the WiFi SSID(User) network you must put a MAC address block of the HomePod. This will prevent the HomePod from jumping to the WiFi SSID(User) network.
- Attach your phone to the WiFi SSID(User)
If you are using HomeKit and are adding accessories you will need to remember to place your phone on the WiFi SSID(IOT) network to add the accessory. Once added you can switch back to the WiFi SSID(User) network.
I would also suggest that you set the WiFi SSID(IOT) network to not auto-join on your phone so that you stay on the WiFi(User) network until needed.
I have all IOT devices, HomePods, Apple TVs and Airplay amplifiers on the IOT network. With the above setup, you can still remote control your Apple TV with your iPhones Apple remote app or HomeKit remote function Airplaying music and video will also work.