DVD recorders do not modulate RF signals. None of them do (with a few rare exceptions). This means whatever is played into or on the recorder does not exit from the coax. It only exits from the s-video, component, HDMI or composite. The coax in splits to the recorder tuner, as well as to the coax out. The coax out is then used for the tv coax in, so that it too can independently tune channels. To connect the recorder to the television (and see the DVD player or recorder picture), you must have s-video, component, composite or HDMI connection. If no such connection exists on the tv, then you must buy a separate modulator, which runs about $20-30 from
Walmart (RCA, Magnavox or Philips branded, in most cases). The external modulator takes the composite or s-video signal, and converts (modulates) it to a coaxial signal for the ancient television.
I have to do the same thing for the tv in my rec room.
Not including a modulation device in a recorder saves a couple of dollars ($5 or less) of production costs. It's BS, but there's not much that can be done about it.