The time variable far-IR/millimeter-wave sky is largely unexplored. However, when PRIMA launches, next-generation ground-based cosmic microwave background (CMB) experiments, including Simons Observatory and CMB-S4, will be operating. These will survey large areas of the sky for transient millimeter sources as a byproduct of their observations, producing regular millimeter-transient alerts. The first results from the current experiments show that they can detect a wide variety of millimeter transients ranging from galactic stars to extragalactic sources associated with active galactic nucleus and other energetic phenomena, and moving solar system objects such as asteroids. These results, and theoretical predictions, indicate that future millimeter/submillimeter facilities will detect many kinds of transients, including flaring stars, protostars, gamma-ray bursts, tidal disruption events, neutron star mergers, fast blue optical transients, and supernovae. New classes of millimeter-variable may be uncovered by CMB experiments, and transient searches at other wavelengths, such as the optical Legacy Survey of Space and Time survey, will produce additional targets to follow up with PRIMA. Predicted rates for extragalactic millimeter transients to be detected by CMB experiments range from 10 s to 1000s of events over the lifetime of these projects. CMB-S4 is most relevant for PRIMA, producing ∼100 extragalactic transients per year. Galactic transients and variable sources will also be detected, but the most common galactic transients, flaring stars, operate on such short timescales that direct follow-up with PRIMA will not be feasible. Variable accretion rates in forming protostars, conversely, produce long-term brightness variations that will be ideal monitoring targets. The addition of mid- and far-IR data points for all these sources can determine much about their radiation mechanisms and underlying physics. PRIMA follow-up of representative examples of various millimeter-transient and variable sources will thus have a powerful impact on our understanding of a wide range of astrophysical phenomena.