We show that the observed evolution of the transmission phase through multielectron quantum dots with more than approximately ten electrons, which shows a universal (i.e., independent of N) as yet unexplained behavior, is consistent with an electrostatic model, where electron-electron interaction is described by a mean-field approach. Moreover, we perform exact calculations for an open one-dimensional quantum dot and show that carrier correlations may give rise to a nonuniversal (i.e., N-dependent) behavior of the transmission phase, ensuing from Fano resonances, which is consistent with experiments with a few (N < 10) carriers. Our results suggest that in the universal regime, the coherent transmission takes place through a single level, while in the few-particle regime, the correlated scattering state is determined by the number of bound particles.