I think suburban deer know all the local dogs very well. Their main trail goes between our fence and the neighbor's and we both have dogs. This is where I have my corn pile and trail camera.
I think both the deer and the dogs don't want to fight and rely on bluffing each other. This time, the dog was barking at the fence as a bluff. When the 3 deer came right to him, he knew it was fight or flight. Since he didn't want to fight 3 adult deer, he retreated.
I'm not surprised the dog eventually backed down. I was surprised that the deer didn't. Especially when they jumped the fence and joined the dog in his yard.