In pump-probe spectroscopy, two laser pulses are employed to garner dynamical information from the sample of interest. The pump initiates the optical process by exciting a portion of the sample from the electronic ground state to an accessible electronic excited state, an exciton. Thereafter, the probe interacts with the already excited sample. The change in the absorbance after pump provides information on transitions between the excited states and their dynamics. In this work we study these exciton-exciton transitions by means of an ab initio real time propagation scheme based on dynamical Berry phase formulation. The results are then analyzed taking advantage of a Fermi-golden rule approach formulated in the excitonic basis-set and in terms of the symmetries of the excitonic states. Using bulk LiF and 2D hBN as two prototype materials, we discuss the selection rules for transitions involving strongly bound excitons, for which the hydrogen model cannot be used.