Why change in magnetic field produces a current
Magnetic force comes from singular magnetic mono-poles that are directly caused by moving (linear, orbital, oscillating, vibrational) mono-charges (singular electro-static charges with one type (+ or -) and a given charge strength or potential). Therefore, moving electro-static charges (especially relativistic impacted) cause magnetic fields.
Therefore a changing magnetic field indicates a changing electric field (pole type to charge type). For EMF this is an oscillating electric field in the photon velocity vector. You can measure this relationship as a change in electric current.