Contour Cable Box AND Separate Cable Modem

Hello,

We have a rental property with Cox internet service.  We have our own Cable modem and router and a working network.  A new tenant has asked for basic cable so we added that service and picked up a "Contour 2" cable box.

The question is how to get my existing cable modem AND the contour box connected.  I did following connections:

Cable to Contour 2 input

Cable from Contour 2 Output to my existing Cable modem input

Should this work?  Because it doesn't.  The cable modem can not reach the internet.

Urgent solution needed.