If your receiver switches to TV Input (instead of staying on the input that the Tivo is connected to) after several seconds after turning your TV on, this is the explanation. The Tivo does not support HDMI-CEC. When a TV that supports HDMI-CEC does not detect that a HDMI-CEC compatible device is connected, it will tell a HDMI-CEC receiver to switch to TV Input.
You can disable HDMI-CEC. But that will also disable ARC. And you will have to add another cable to get audio from the TV to the receiver.
The best solution is for Tivo to implement enough of the HDMI-CEC spec to keep the TV from deciding to change the receiver's input.
There are other threads complaining about the lack of HDMI-CEC support in the Tivo. I am detailing a real world problem that this is causing. This is going to become more and more of an issue as people buy new TVs that support HDMI-CEC.
Here is another thread with further explanation and additional work arounds: