We have studied a strongly coupled quantum dot-micropillar cavity system subject to an external magnetic field. The large diamagnetic response of elongated In_{0.3}Ga_{0.7}As quantum dots is exploited to demonstrate magneto-optical resonance tuning in the strong coupling regime. Furthermore, the magnetic field provides an additional degree of freedom to in situ manipulate the coupling constant. A transition from strong coupling towards the critical coupling regime is attributed to a reduction of the quantum dot oscillator strength when the magnetic confinement becomes significant with regards to the exciton confinement above 3 T.