If you use a compass app you need to treat it EXACTLY like a real compass - you hold the phone/compass NO WHERE NEAR the mount, otherwise it will be influenced by the magnetic field of the motors, any ferrous material in the mount etc. IF I use an app, I stand about 5 feet behind the mount and eyeball it. If I use a compass, I have come to know the usual amount of deflection next to my mount, so compensate for it. I made a special plastic jig to hold the compass in a repeatable position on my mount dovetail during setup, starting with a hand held rough align with the tripod, followed by the compass in the jig with azimuth bolt refinement.
I have used both in the field to good success. I also use SharpCap to run an alignment routine to nail it after the rough compass alignment.
I take it you remembered to subtract the magnetic declination from the app display?
(silly question,but I have seen it where people have forgotten). One or two of the better compass apps lets you switch between TRUE and Magnetic. No brainer to use TRUE. (as I recall in Sippy Downs/Sunshine Coast area, you need to subtract 11° from the magnetic - compass or app needs to show 169°)