2 angry cats

I have 2 male cats who were both neutered about 6 months ago. I just moved to a new place and there is a male cat who lives next door. My cats are strictly indoor and the neighbour is outdoor. He keeps coming and spraying on my porch. I let my cats come out with me one day to see how they would react. There was a little growling but for the most part they were ok. I only let them out for about 2 min. When they came back in the bigger of my 2 was a little angry. He just seemed to be smelling the other cat still inside. That was about 2 weeks ago. They have both been fine since. Today, the neighbour cat was out on the porch so I decided I would let them try again. This time I only let one out at a time. Both cats were fine. They both came back in and kept on playing. 10 min. later I let them out again, this time all hell broke loose. The bigger of my 2 charged at the neighbour. My smaller one came out to see what the commotion was . In the mean time I went and grabbed my bigger cat and brought him inside. He was freaking right out. He started peeing and he pooped on the floor all over the place. Now my 2 cats can't get along AT ALL!!! I don;t know why they have turned on each other. PLEASE HELP!!!!!!!!!! Tweet