No, when using Thinka with HomeKit, there is no need for any connection outside your home network. Only Siri does need an Internet connection to process your voice commands. So when you would decide to block Thinka from accessing the Internet all together, it would still work with your iPhone.
Amazon and Google however do run their smart home solution in the cloud.
Thinka itself will check for updates regularly on the Thinka repository. During installation the Thinka setup just helps you find your Thinka on your local network, where all installation is done.