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By conducting helicity-dependent ultrafast magnetization dynamics in a CoTb ferrimagnetic alloy, we are able to quantitatively determine the magnetic circular dichroism (MCD) and resolve its role in the helicity-dependent all-optical switching (AOS). Unequivocal interpretation of the sign of the dichroism is provided by performing AOS and femtosecond laser-induced domain wall motion experiments. We demonstrate that AOS occurs when the magnetization is initially in the most absorbent state, according to the light helicity. Moreover, we evidence that the MCD creates a thermal gradient that drives a domain wall toward hotter regions. Our experimental results are in agreement with the purely thermal models of AOS.