It sounds like you need a HomeKit hub for remote access. When you're home, your phone acts as the HomeKit hub for your Mysa. When you leave, your HomeKit hub goes with you, leaving no way to access the thermostats via the Apple Home App. You can verify your thermostat is still connected to WiFi by opening up the Mysa App and seeing if it's still online when you're remote.
The good news is you don't need to buy a new device. Your HomePod, Apple TV 4K, Apple TV (4th generation), or iPad (with iOS 11 or later) will do the job.