We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotatingboxlike circular trap, i.e., states where vortices in one species host the atoms of the other species, which thusplay the role of massive cores. Within a fully analytical framework, we calculate the equilibrium distancedistinguishing the motion of precession of two corotating massive vortices, the angular momentum of eachcomponent, the vortices healing length, and the characteristic size of the cores. We then compare these previsionswith the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations.Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive coreswhich they host thus conveying their same motion of precession, but that there is no evidence of tangentialentrainment between the two fluids, since the cores keep their orientation constant while orbiting.