Magnetic shape memory Heusler alloys are multiferroics stabilized by the correlations between electronic, magnetic and structural order. To study these correlations we use time resolved x-ray diffraction and magneto-optical Kerr effect experiments to measure the laser induced dynamics in a Heusler alloy Ni$_2$MnGa film and reveal a set of timescales intrinsic to the system. We observe a coherent phonon which we identify as the amplitudon of the modulated structure and an ultrafast phase transition leading to a quenching of the incommensurate modulation within 300~fs with a recovery time of a few ps. The thermally driven martensitic transition to the high temperature cubic phase proceeds via nucleation within a few ps and domain growth limited by the speed of sound. The demagnetization time is 320~fs, which is comparable to the quenching of the structural modulation.
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