We study the problem of characterizing mode dependent dwell-times that guarantee safe and stable operation of disturbed switching linear systems in a model predictive control (MPC) framework. We assume the switching instances are not known a priori, but instantly at the moment of switching. We first characterize dwell-times that ensure feasible and stable switching between independently designed robust MPC controllers by means of the well established exponential stability result available in the MPC literature. Then, we employ the concept of multiset invariance to improve on our previous results, and obtain an exponential stability guarantee for the switching dosed-loop dynamics. The theoretical findings are illustrated via a numerical example.