I know the experiment you're referring to. It's been a long time since I've seen it, no idea how to find it now, but you're definitely misremembering some details. Dogs do have a sense of time, but in that experiment, it actually had to do with scent. As their owner was away, their scent would gradually dissipate throughout the day. At a certain point, the scent was weak enough that the dog knew it was about time for their owner to be home.

In the experiment, then they did everything they could to remove their owners scent from their home. The dog's owner came home at the usual time, but the dog wasn't expecting it this time because they had removed the owner's scent earlier, so the dog was clearly surprised and confused.

Dogs have a very strong sense of smell which we humans often fail to appreciate. It's not like dogs can smell their owner coming home from miles away, that's a little preposterous. But they can use their sense of smell in other ways, which are not so obvious to us, such as to maintain a sense of time.