On a California part-year resident return, you allocate all income and deductions that are atrributable to California-sourced income, and all world-wide income and deductions for the days you were a California resident. So Turbotax is correct, if you paid 1-2 months of mortgage interest on a out of state property while you were still a California resident, that allocable interest is deductible on your California part-year return.
https://www.ftb.ca.gov/forms/misc/1100.html
