It’s ok to test out by installing the TinyCam on your phone, but you would want to install TinyCam on a dedicated device because the TinyCam is basically like a video streaming proxy server. TinyCam gets the video streaming from the web cameras, transcode the video and then serves the video streams through its web server.
Ring is a closed system, so TinyCam won’t be able to stream videos from Ring though. But you can surely create a dashboard for wyze and eufy cams’ live streams, and create a rule to redirect to this dashboard automatically when a motion is detected if you are using Fully Kiosk Browser to run your dashboards.
If you can share the the steps you have tried and the specific questions you have in the process, we may be able to provide better help and more detailed instructions. 