They CAN use your router. I did an install in a 7000 SQ FT mansion last week. 1 Hopper 3, 3 WiFi joeys and one of them was too far away to stay linked to the WAP. so I set them up with 3 Velop Mesh Nodes. One at the Frontier Gateway, one halfway to the furthest WiFi Joey and 1 at that joey with Ethernet connected to the joey - boom! popped right in. I told them just hope the internet doesn't go down.
Sometimes we can suffer the same issue but from different causes. In my case, when turning on the TV with the wireless Joey and seeing all the pixilation, I tune the TV to an OTA channel for a few seconds than back to where I was and everything is than OK. I have no idea what happened or why this clears it up, but it always works.