By default cloud. However, it supports HomeKit and @SmartHomePrimer described recently how to use Home Assistant to bring these into Hubitat locally in this post:
I don't have this hub - I have two of the Mijia hubs, and I didn't need internet access to either pair the devices or use them. I would bet the Aqara hub is similar, but @SmartHomePrimer would know for sure.
Been there. Done that. They are more stable with compatible repeaters, but no where near as stable as on an Aqara/Mijia hub.
Edit: BTW, that Aqara hub is much cheaper on AliExpress