I have installed the Rialto thermostat. The thermostat, white box, smart box are all connected. But the boiler doesn’t turn off, so the thermostat is not controlling the boiler. But I can use my photNe to turn off the boiler
I’m confused by your question?
If the Rialto app can turn off your Boiler, then the thermostat is controlling the boiler.
From my searching the Rialto doesn’t natively integrate to Home Assistant.