I'll try to clarify the time signal mess. I understand how confusing it can be.
First, back in the analog era, there was a time signal carried by many PBS stations. That's long gone, but any analog signal can carry a similar time signal. For example, my old SD satellite receiver outputs the analog time signal, and I have an old VCR getting its time from that receiver to prove it. It's possible that Cox also does this on one or more of their analog channels, if they have any left.
Second, for digital over-the-air, there's a time signal included in each station's PSIP. Note the difference: with analog, there was one station (typically PBS) broadcasting a time signal. With digital, each station broadcasts its own time signal. PSIP is the only time signal supported by the Homeworx or iView: they don't even have an analog tuner, so they couldn't possibly support the old analog time signal even if it's available.
For the Homeworx or iView to start a timed recording, an accurate PSIP time signal must be available on the station it's tuned to. That's the station it "listens" to in order to start the recording. A time signal on another station wouldn't help.
Third, cable companies don't generally rebroadcast OTA digital signals unmodified. Instead, they extract the streams they want and multiplex them onto their own digital channels. Unfortunately, this process drops the PSIP info from the OTA stations.
A cable company could insert its own PSIP onto its QAM channels, but many don't. Instead, they use their own cable industry standards for the functions that OTA stations use PSIP for, including time. The Homeworx, iView, and in fact most clear QAM tuners don't support those cable standards. That's why the Homeworx and iView don't work well with most cable systems.
In short, Cox is probably sending the time, but not in a form that the Homeworx or iView can use. The Homeworx and iView need PSIP, and they need it on every station.
Clint's local HD channels (e.g., channel 712) are QAM. His SD channels, 2-99, could be QAM or analog. (Probably mostly QAM, but I wouldn't be surprised if at least some turned out to be analog.) The Homeworx and iView will receive the QAM channels (but not any analog ones). However, without PSIP they will almost surely have different channel numbers. A cable user would just have to tune through all the channels (potentially hundreds) and find out which ones are which. (Many will turn out to be scrambled channels, which can just be deleted of course.)
One last thing: it's important to understand that the Homeworx and iView don't have a "clock," in the sense of a gadget that keeps reasonably accurate time once you set it. They rely on PSIP time being broadcast continuously. (It's more like a stopped clock that gets reset every second!) It might be possible to rig a true clock in the firmware, if there's some periodic interrupt occurring at the hardware level, but no guarantees - and even if possible, it could still take a major rewrite of the firmware to enable a true clock. So I wouldn't hold my breath.