The thinking of paying primary mortgage first is.

The first is to reduce your rental property positive income to zero so that you don't have the tax liability on your rental.  The only time that paying down the rental mortgage makes sense is that you have a negative cash flow on the rental.

The other consideration is by paying down your primary residence mortgage that you will have an easier time and a better rate to pull the equity out of your pirmary in the future.  Just in case you want to do another investment.