If the masses have watched Apollo grow up, they have seen his tantrums as well as his triumphs. Since he is destined to be their leader, the regular people have a lot of opinions about him. If the Emperor hates Apollo, the father would have manipulated the feed to show an unflattering/ petulant version of Apollo. To prevent an overthrow or limit Apollo's support.
And the Emperor would use the press to present himself as a benevolent but fierce ruler, so few realize that he is cray-cray.
This is a logical extension of the press and a novel way of using real-time TV. It would make sense that a crew or a bot is following Apollo everywhere. Dunno, but this is a lot more futuristic to me than the smart-eyes. Our reality TV doesn't follow Trump during his life at the White House, though I'll bet he's thought of this wrinkle. It would get great ratings and might tone down the resistance from intellectuals who think they are keeping tabs on him.
I think Apollo and even his father would oppose constant monitoring, since it would allow the enemy to figure out how to play him once he's in power. The Julii are nothing if not orchestrators of their public image. I'm pushing the limits just by considering a public match with Caligula and the Shogun. Even in Dune, the Baron's nephew, Feyd, a remoreless killer, only ever went up against drugged opponents. If the emperor wants to put out false videos, you need little more than an Amiga 1200. After all, Apollo faked his death the same way. Consider the resurrection of Grand Moff Tarkin in the latest Star Wars film. In ten years, give or take, the tech will make fake videos indistinguishable from the real thing.