TiVo isn't provisioned on separate anything from residential broadband services nor does it have any dedicated bandwidth, it's a standard best effort configuration and contends with whatever else is on the channels as normal
Unsure why speeds would dip at peak, sounds like a coincidence especially given the TiVo will be on the DOCSIS 1.1 network while the 20Mb will almost certainly be served via the overlay DOCSIS 3 network.