It's not a simple situation to understand, however you cut it -- the field around the object is very inhomogeneous, the induced voltage is the derivative of the change in field (Faraday's law), good old fashioned field geometry, and etc.
I would guess the double-peaked response comes from a flat shaped object, where the first corner passes (field is more intense around corners of permeable objects), then as the corner is (nearly) underneath the centerline of the sensor, voltage crosses through zero (flux change is zero), then it reverses as the field is less along the breadth of the object, then it peaks again in the opposite manner as it leaves.
Suffice it to say, there's a blip of some sort, and detecting it with a high-pass filter and comparator should be adequate. More advanced signal analysis could be done (e.g., curve fitting to find the geometric center of the blip, at any RPM and ambient noise level), but that would be fairly heroic effort for little gain.

Tim