We present 0.3 (band 6) and 1.5 (band 3) ALMA observations of the (sub)millimeter dust continuum emission for 25 radio galaxies at 1<z<5.2. Our survey reaches a rms flux density of ~50$mu$Jy in band 6 and ~20$mu$Jy in band 3. This is an order of magnitude deeper than single-dish 850 $mu$m observations, and reaches fluxes where synchrotron and thermal dust emission are expected to be of the same order of magnitude. Combining our sensitive ALMA observations with radio data from ATCA, VLA, and IR photometry from Herschel and Spitzer, we have disentangled the synchrotron and thermal dust emission. We determine the star-formation rates (SFR) and AGN IR luminosities using our newly developed spectral energy distribution fitting code MrMoose. We find that synchrotron emission contributes substantially at ~1 mm. Through our sensitive flux limits and accounting for a contribution from synchrotron emission in the mm, we revise downward the median SFR by a factor of 7 compared to previous estimates based solely on Herschel and Spitzer data. The hosts of these radio-loud AGN appear predominantly below the main sequence of star-forming galaxies, indicating that the star formation in many of the host galaxies has been quenched. Future growth of the host galaxies without substantial black hole mass growth will be needed to bring these objects on the local relation between the supermassive black holes and their host galaxies. Given the mismatch in the timescales of any star formation that took place in the host galaxies and lifetime of the AGN, we hypothesize that a key role is played by star formation in depleting the gas before the action of the powerful radio jets quickly drives out the remaining gas. This positive feedback loop of efficient star formation rapidly consuming the gas coupled to the action of the radio jets in removing the residual gas is how massive galaxies are rapidly quenched.