Agreed, first thing is to check for medical issues. The stress of having another cat around could contribute to a UTI developing. On the other hand, he may be responding territorially. But doing the medical check is the first things to rule out.
Also, you need to make sure the areas he's peeing on are cleaned with an enzymatic cleaner like Nature's Miracle. It breaks down the urine into it's basic elements so the cat can't smell it. If you don't do that he can still smell it (even if you can't) and will think it's OK to go there again.
I'm going to move this thread to Behavior for you....
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Holly, Misty & their friend, Jake, the dog.
Onyx, Callie May, Maggie & Kobi forever in my heart.
Yes, I know I need a new signature pic...someday...