Neutered, but not acting like it.

I have a concern about my 2 year old gray tabby, Buddy.

He is neutered and has been for a while. We adopted him after he magically appeared at our doorstep and not going away (That tends to happen to us alot.), but anyway after we moved in november and brought all 3 of our cats with us (Little One, Baby, and Buddy).
About 3 or 4 months ago we welcomed another cat (actually kitten about 5-7 months old) She was our neighboors kitten, but we fed her on the side because it didn't look like they gave her much attention, they would just leave her outside days at a time.
So anyway Buddy was great friends with her, as he is a very social cat. But one day this little kitten, Julie, was in heat and there were several toms around our house, apprently sensing her. She never showed any signs of heat and we would often catch her with a tom on top of her, but she would be yowling as if in fear, like she didn't like it. We tried to chase off the toms often.
But anyway, one day while I was outside monitering Julie while she was outside (she had to use the bathroom), there were at lest three toms around us and watching Julie's every move. Buddy was out there also, just sitting around. Then, in front of the toms, Buddy jumped on top of Julie, as if he was trying to mate with her. I was shocked because he had been neutered for a while and this happened twice this day, so I was thinking since he did it in front of the toms, was he showing that Julie was hers and protecting her from the toms? Or is is possible they could have missed something when he was neutered?

Also what I have noticed is that he has very big testicles, rather larger than my other two neutered males. And also he is very vocal when he walks into a room. Another thing is he gets really violent sometimes when you pet him. But other times he's loveable and really sweet. My parents joke that he is "bipolar" and just has a little wild in him, as that's the best bet where he was born. Any ideas?

If he is neutered he shouldnt have any testicles!!!

You should spay Julie ASAP, because if she isn't pregnant already, she will get soon. Also, it could be a dominance issue. A way for a cat to show dominance is to grab the other cat by the back of their neck. Neutered cats do it to other cats as well. Is there any way Buddy isn' t neutered, though? Did you take him for the procedure yourself?

You say you noticed he has big testicles? But they should be gone if he is neutered. Did you mean scrotum (the sack the testicles are in)? Hoo boy, that would be something if all this time you thought he was neutered but he wasn't!!

Yes, I did go with my mother when we took him to get neutered. He was neutered at the same place my other outdoor-indoor cat, Little One was neutered and he is not showing the same behaviors as Buddy is.

I'm guessing it's the sac, because his is a little smaller than a feral cat's behind, but way bigger than my two other neutered males. But it still looks a little like testicles to me, because they have a defined round shape to them.
Also, he is a bit thin, kind of like you would see in a slender feral.

As for Julie, we were having financial problems at the time, so we couldn't spay her right away. But we did keep her indoors for a while but she escaped under my father's feet and dissappeared for a whole day and ended up getting pregnant. She's already had the kittens (3) and we already have the money and are planning on getting her spayed after the kittens are weaned. And the kittens are going to the SPCA around 10-12 weeks old (they'll be 5 weeks tomorrow.)