  Using Soft-Collinear Effective Theory, we develop the
transverse-momentum-dependent factorization formalism for heavy flavor dijet
production in polarized-proton-electron collisions. We consider heavy flavor
mass corrections in the collinear-soft and jet functions, as well as the
associated evolution equations. Using this formalism, we generate a prediction
for the gluon Sivers asymmetry for charm and bottom dijet production at the
future Electron-Ion Collider. Furthermore, we compare theoretical predictions
with and without the inclusion of finite quark masses. We find that the heavy
flavor mass effects can give sizable corrections to the predicted asymmetry.
