We report a comprehensive study of exciton confinement in self-assembled InAs quantum dots (QDs) in strain-engineered metamorphic In_xGa_1-xAs confining layers on GaAs using low temperature magneto-photoluminescence. As the lattice mismatch (strain) between QDs and confining layers (CLs) increases from 4.8% to 5.7% the reduced mass of the exciton increases, but saturates at higher mismatches. At low QD-CL mismatch there is a clear evidence of spillover of the exciton wave-function due to small localisation energies. This is suppressed as the In content, x, in the CLs decreases (mismatch and localisation energy increasing). The combined effects of low effective mass and wave-function spillover at high x result in a diamagnetic shift coefficient that is an order of magnitude larger than for samples where In content in the barrier is low (mismatch is high and localisation energy is large). Finally, an anomalously small measured Bohr radius in samples with the highest x is attributed to a combination of thermalisation due to low localisation energy, and its enhancement with magnetic field, a mechanism which results in small dots in the ensemble dominating the measured Bohr radius.