Aggressive outdoor pet cat

The people who live a couple of houses away from us let their two pet cats (neutered males) roam outside. They come into our yard occasionally, and they also come eat the food I put out for the other feral cats. It irritates me a little, because these guys have a home and regular food indoors, but I figure that as long as they don't eat everything, I'll tolerate it. It's not like I can do much about it anyway.

The problem is that sometimes they are very aggressive toward Mittens, who is the feral cat who regularly hangs around our house. Earlier this evening she was napping on a low wall in front of our house. We saw one of the neighbor's cats in the backyard coming toward the house. So we went to look out a front window to see if he came around to the front of the house, which he did. Mittens was awake and watching him, and hissed when he approached. She got very low to the ground. Will sort of sat and watched her, and then all of a sudden he pounced. She got away and went up onto our porch. At this point I decided to intervene as Will was also heading to the porch. I went outside and did the Mean Nasty Human act, waving my arms at Will and shooing him, and told him to go home. I didn't yell, but he decided not to mess with me and left. Mittens seemed fine after he left, so I don't think he actually hurt her at all.

I feel kind of bad for shooing him away like I did; he is a pet, after all, and I don't want him to be afraid of me. And I'm not sure I really did the right thing, coming to Mittens' aid like that. She has to deal with these cats all the time when I'm not home and not watching over her. I really wish the neighbor would keep their cats indoors. They seem to have more confidence outdoors, and are very bold. There was a time when Mittens was the bully, but lately she has been the bullied, rather than the bullier.