OP was asking about recommendations for "Most accurate IOS app for turntable speed check". Well, as @dover correctly pointed out, these apps are not accurate:
RPM and other apps I have tried are not accurate. Results are inconsistent. They are only good for entertainment - not calibration.
Just for giggles, I once installed RPM on two phones, then placed both phones on a spinning turntable with the apps running. The speed readings were different. What’s worse, the delta between the two readings was not constant.
My uneducated guess is that the inaccurate readings are a function of the phone hardware rather than the app itself; but in any event, these apps are not fit for calibration.

