We are not sure if DJI has any "official" start-up method that they publish but with all UAVs we have always instructed and informed to power on your RC first and then the aircraft. This was always the standard in other radio controlled vehicles as well and personally I just objected that practice with the very first drone I built.
With Inspires, Phantoms, Mavics, Sparks it is pretty safe to say that any start-up order works without issue. We've found that on the Matrice 210 running dual payload, Cendence and CrystalSky it is very important to have our Cendence powered on first with CrystalSky running your respective app and then powering on the aircraft from there.
There's some good discussion regarding start-up procedure on the MavicPilots forum here:
Confusion over start-up procedure and this would be just as applicable to Inspire as well.
Here's a nice graphic from @AlanTheBeast over there. App before RC could really go either way in our opinion.
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We will add that every time we've flown with DJI reps it has always been RC before aircraft. We've also seen DJI reps online confirm RC before aircraft but as for an "official" publication from DJI we are not aware of any document or instruction guidelines for this subject.
We hope the above information helps, good discussion, and don't hesitate to ping back with any further questions.
Safe flying, all!

–The Advexure Team