I have two of the zigbee Inovelli Blue Series VZM35-SN fan switches. I recently migrated them from the Tonesto-Homebridge app to the native HE Homekit integration. Homekit does not seem to display the fans as off when the switch is OFF, rather it still displays the speed at which they're set, reflecting them as still ON. It appears from their Device page, that the switch has independent attributes for the switch versus speed, so the switch can be off, but the speed attribute maintains its last setting, which I assume is where the HE Homekit integration is pulling its status. It previously worked fine under the Homebridge app.
C8 - 2.5.0.135
Sounds like a problem with the Inovelli driver, as "off" is a valid fan speed and should match the real-world state of the device (the "switch" capability is entirely superfluous, though is sometimes found in drivers like this since it's a bit more widely usable than this more specialized capability). Are you using their driver?
I played around with the device settings, and found more information than you probably want to read, but... Yes, I am using the Inovelli driver. I noticed this situation because I have a rule that shuts off the fans at 11:00pm if they're still on. It displayed fine with Homebridge, but when I migrated to the HE integration it appeared the fans were still "on", although the fans had actually shut off.
From the device page I tried to set the speed, but it would not change if the switch for the fan was already OFF. It would only allow me to change the speed when the switch was ON. I just changed my rule to set the speed to OFF, rather than the switch, and that's doing the trick. The switch also sets to OFF after the speed is set to OFF. The fans restore to their previous speeds when the switch is turned back ON.