Retirement tax questions

I moved out of Utah but had a rental home in Salt Lake. I was told that if I claimed the residential exemption that I would have to pay Utah Income Tax for ALL money I made regardless of where I made it. This means that I would have to pay Utah income on money I'm making from my employer in another state, a state which is also charging an income on that same money.  Has anyone else had to deal with this?  Is this true? If so, where is the Utah code that clarifies this?