No, a nonresident of California needs to report only California source income. In your case, it is the rental income.
Nonresidents of California find that TurboTax adds back all the HSA contributions, even ones made in another state.
There is no good way for TurboTax to know in which state the contributions were made in, so the taxpayer needs to manually adjust the California state income to remove the HSA contributions that were added back while the taxpayer was not in California.
***To make the CA adjustment***
Go to State Returns, and navigate to your California return.
In Income and adjustments, proceed through the interview. You may see a screen announcing that HSA contributions are treated differently in California. Just hit Continue.
You will notice on the main page ("Here's the income that California handles differently"), the first line item is (likely to be) "Health Savings Account (HSA) Contributions". Here TurboTax notes that the amount of your HSA contribution has been added back to the California return.
NOTE, despite the Edit button, you can't change this here.
Scroll down to Miscellaneous Adjustments on this screen. Click Start for Other Adjustments to Income.
Enter in the left column "adjustment for out-of-state HSA contributions". Enter in the middle column (i.e., a subtraction) the dollar amount of HSA contributions made out-of-state (in your case, all of them). This will be subtracted from your California state income.
Make a note on your copy of your state tax return (because, of course, you are going to save a copy, right?) that you made this adjustment because TurboTax added back all the HSA contributions (even ones made while a non-resident), and you needed to counteract this. This is in case you ever get a letter from the state asking about this adjustment.
