You're doing fine.
When the magnet is somewhat away from the pole piece the attraction and repulsion you feel are what you're looking for: coil-induced pole piece magnetization working against the probe magnet. Use these forces to figure out which poles on the stator are which and whether you've got your coils hooked up in the directions you think you should.
When the (STRONG) magnet is too close to the stator pole pieces it induces more magnetization into them than the current in the coils does. So you always feel an attraction. (It's stronger when the coil magnetization and the induced-by-the-probe-magnet magnetization add, weaker when they subtract. But the difference probably isn't enough to feel.)
The weaker magnet of a compass won't induce enough magnetization to foul the test. On the other hand it will also be sensitive enough to detect residual magnetization in the stator core. That may confuse the issue when you're probing a pole piece that "isn't magnetized" by the coils. So you're better off using a stronger handheld probe magnet, where you can feel the strength of the attraction and repulsion, and hold it far enough away for the test to work.
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