IMO, the grain bed temperature should be your target. I use a direct fired RIMS and do a continuous circulation while mashing. My kettle has the typical large dial thermometer with a 4" probe into the mash about 5 inches up from the bottom through the kettle wall. The probe is not quite in the center of the mash, but it's close enough and this is where I monitor the grain bed temperature. I also monitor the returning wort passing through the cpvc manifold above the mash using a continuous reading digital thermometer. When simply holding a steady mash temperature I circulate at about 1-1/2 gpm with the burner on a very low setting. The returning wort should be about 3 F above the target mash temp as there will be some losses along the way down through the mash. I monitor the dial thermometer and as I approach my target temperature I reduce and finally shut off the burner and let it coast. Usually the mash temp will stay very constant and drops only very slowly. As soon as I notice any drop in temp, I re-ignite the burner and adjust the returning wort to a degree or two above the target. Most of the time little or no adjustment is required once you reach the target temp. When ramping up the temps I shoot for 5 or 6 F above the target temp. This allows a reasonable temp gain while avoiding overheating or scorching the wort. The faster you circulate the more heat you can apply while still keeping the return wort only a few degrees above the desired target temp. The tricky part is circulating fast, but not so fast that you stick the mash. I'm installing a vacuum gauge on the kettle output to monitor the pump suction. I want to push the limit on the recirculation rate and needed a way to monitor the suction with more precision. Previously, I simply watched the return flow and made flow rate adjustments more by guessing than anything else. You don't know where the limit is until you exceed it. I've also learned not to overcrush the grain and getting that right took awhile.
So, yes do want to "overshoot" the wort temperature to maintain the grain bed temperature. Patience is required because it will take several minutes at least for adjustments to register on a thermometer monitoring deep in the mash. It takes some time for the heated wort to make it down through the mash at the rates we are pumping. Hence, the need for a reasonably fast pumping rate.