The magnetic phase transitions in the FeMnP1-xAsx compounds with x= 0.25, 0.35, 0.45, 0.50, and 0.55, have been studied by iron-57 Mössbauer spectroscopy. The ferromagnetic and antiferromagnetic spectra have been analyzed with a model that takes into account the random distribution of the P and As near-neighbor anions of a given iron site. This distribution is a binomial distribution of the contributions to the spectra of each iron with n As near neighbors. A magnetostriction model has been used to characterize the temperature induced paramagnetic to ferromagnetic first-order phase transition and order parameters, ηF=2.6, 2.3, 2.0, 1.57, and 1.43 have been obtained for x=0.25, 0.35, 0.45, 0.50, and 0.55, respectively. A detailed phase diagram has been derived from the Mössbauer spectral analysis and reveals a magnetic triple point at x= ~0.35 and ~210 K. A model that takes into account the random binomial P and As distribution and the contribution from the iron and manganese magnetic sublattices yields excellent fits of the spectral components assigned to the ferromagnetic and incommensurate antiferromagnetic components for the x=0.25 and 0.35 compounds at all temperatures.