Dear @Cameri Yes sphericity test replaces homogeneity test in case of Repeated Measures ANOVA (RMA). In t-test or one-way ANOVA, assumption is that variance among the groups is assumed to be equal whereas in RMA, the assumption is that equality in variance exists across the different repeated measures.
The short answer is that nothing has changed but now there are more dimensions that required a somewhat new multvariate test which is about the same as the old one.