Only one Line runs from the ONT to the router (modem), the remaining ports on the ONT are not active, Since I have an unfinished basement the tech ran one cat6 cable from the ONT and battery/power supply upstairs to the router.
He then ran a 4 port switch off of the router for my TV's (STB's) then ran the cat 6 cables for the STB's from that switch back into the basement completed the run to the separate rooms, and brought the cable back upstairs in each of the rooms I wanted tv, he actually put an Ethernet jack on the baseboard.
Had the technician decided it was easier to use existing coax cable he would have simply run one coax cable from the router(modem) upstairs back into the basement and tied into the main splitter coax..
However each install is pretty much 100% custom and they will work with you to place the equipment to suit both yours and their needs.
My install was 2 years ago, at the time I asked him why he used a switch for the TV runs instead of using the available ports on the router, he said this way it leaves me with extra ports to hook other devices onto the internet if I want.