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It doesn't really matter to be honest. People here say turn remote on first before drone etc but it honestly makes no difference otherwise it would be emphasied in the manual. You still get RTH position and fly without issues any way you do it so long as you let it acquire RTH before take off. Try it yourself, it makes no difference. Just be sure to get gps and rth set before flying off and you're good to go.
For what it's worth I have my phone (Galaxy S10) unlocked but do not manually start the app. I turn on the controller then the drone. Shortly afterward the DJI Fly app starts up automatically and I'm pretty much ready for action as soon as the RTH position is acquired. I'm so used to old school RC planes and heli's that it's hard for me to have the aircraft switched on without a valid transmitter signal present.
With radio-controlled models, pretty much everybody follows the rule of turning on the transmitter, then the receiver (and the opposite when turning off). With old radios it was a must, but even with modern ones, where the receiver is paired with a transmitter and should not pickup other signals or interference, you basically don't want to the model to sit there, powered up, without controlling signal. I don't care if DJI doesn't recommend it, I consider it good practice anyways.
EDIT: just saw RCnerd's post... saying exactly the same thing...