DIS in electron-ion collisions provides detailed information on nuclear parton distribution and the partonic dynamics and hadronization in the cold nuclear matter. A general-purpose event generator that accounts for in-medium parton dynamics in DIS benefits both phenomenological study and experimental design. In the eHIJING-1.0 model currently under development, we use Pythia8 to generate initial hard collisions. The struck quark undergoes multiple collisions in the cold nuclear medium. We model the in-medium collision kernel by a saturation-motivated transverse-momentum dependent (TMD) gluon distribution function. In particular, the TMD distribution and saturation scale are determined self-consistently and results in an $x_B$ and $Q^2$ dependence of the jet-transport parameter. Medium-induced parton emission, using either the collinear higher-twist or the generalized higher-twist formula, is added to the $p_T$-ordered parton shower of Pythia8. Finally, we account for medium-modified fragmentation by allowing induced gluon emissions at low-virtuality before hadronization takes place. We tune and validate that the eHIJING model provides a satisfactory description for hadron multiplicities in e-A collisions at the HERMES experiment. We make further predictions for future EIC.