Adding Tisbe pods to your fishless reef should be fine and they should multiply. IMO tisbe pods are the best copepod for Mandarins to feed on. Tisbe pods spend most of their time on the rock and substrate which is where the mandarin feeds. Other pods like Tigger spend most their time in the water column. How often do you see a mandarin eating from the water column?
Having your pods eating detritus is fine and a Mandarin will survive off of copepods that eat detritus but I recommend feeding your tank a phytoplankton that the tisbe pods will consume. Copepods are like anything else, they are what they eat and phytoplankton is much more nutritious then detritus which makes a more nutritious meal for the mandarin.