I think you're making an assumption that the cat was somehow bothering or harassing your chickens. You don't know that. You didn't see that. All you know is your chickens were raising a ruckus and you saw a cat leaving your backyard. It's a pretty large leap from seeing a cat leaving your yard to say it was harassing your chickens. Perhaps it was the other way around, i.e, the chickens were harassing the cat as it happened to be strolling by or that they were just reacting to something to which they're unfamiliar.
My cat, who is an absolute murderess, is afraid of the chickens. No neighborhood cats nor any of the feral cats around ever bother the chickens. Would I trust a cat around young chicks? No, but a six month old chicken has little to worry about from a cat, IMO. I'm not saying it can't happen or even that your neighbors cat wasn't bothering your chickens, but be sure of the circumstances before drawing conclusions which you can't support.