This is correct: both states tax you. Your resident state (PA) will tax you on all of your income regardless of where it is earned. Your nonresident state (GA) taxes all income sourced from that state. For most, "sourced" income is the amount of income earned while working in the state, such as wages or self-employment. Pension, unemployment, and other similar income received from Georgia would not be Georgia source income for tax purposes. On the resident state may tax these types of income. Rent, however, is sourced in the state where the rental property is located. Thus, Georgia will tax your rental income as a nonresident.
For this reason, you will file two personal state returns: A Georgia nonresident return, and a PA resident return. Pennsylvania will, however, issue you a credit for the amount of income you earned from Georgia and which Georgia taxes. Complete the Georgia return first so that the credit for PA calculates correctly.
Here is an FAQ which discusses this topic in more detail: https://ttlc.intuit.com/replies/4777207
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