The miniscule Texas State Guard, DPS and Texas Rangers report to the Governor, the NATIONAL Guard is funded by Fed and reports to the POTUS unless assigned otherwise. If you have verifiable linkage otherwise, please let us know.
No, the National Guard does not always report to POTUS. When they operate under State Active Duty status, they report to their respective state governor. They ONLY report to the federal military chain of command when they are nationalized under Title 10. When they are nationalized under Title 32, they still report to state governors.
They also are not always funded by the federal government. When a state governor calls out the NG for duty in-state, it is at State expense. Each state must reimburse the federal government for certain expenses. If they are nationalized under Title 10 or 32, they are funded by the feds.