Retirement tax questions

Not trying to beat a dead horse here, but do want to ensure clarity.  I'm doing my son's taxes--he's in college in another state and filed two returns last year for our home state (on summer income) and the state where he's going to college.  We received a 1099-G for his out-of-state refund.

 

Because he took the standard deduction, he does not/not need to report the 1099-G for the refund.

 

However, if he did not take the standard deduction, we would only report the payments made to the one state that provided the 1099-G, right?  We would not include payments made to the other state.

 

Thanks for your patience with the amateurs.