A valley-selective circular dichroism and a pronounced spin-valley locking in monolayer transition metal dichalcogenides (TMDCs) enable the investigation of new many-body physics revealed in the ultrafast nonlinear optical response of these atomically thin materials. While this topic is experimentally well studied in pump-probe spectroscopy, only a fragmented theoretical understanding is available due to the complexity and multitude of occurring effects. Here, a microscopic approach is presented to describe the ultrafast pump-probe response of monolayer TMDCs in the coherent limit. We focus on close to band edge excitations dominated by strongly correlated, bound electron-hole pairs, namely excitonic excitations. The approach includes Hartree-Fock and correlation effects up to two excitonic excitations known from conventional semiconductors as well as TMDC typical Coulomb mechanisms such as intra-and intervalley excitation and charge transfer. The investigated coherent limit is able to explain different signatures observed in ultrafast pump-probe spectroscopy for temporal pump-probe overlap within one consistent formalism dominated by excitons, biexcitons, and exciton-exciton scattering states.