I found this information about the Carmine Jewel Cherry.
It does not require a pollinator to produce fruit, but having another cherry (Nanking, sandcherry) nearby will increase productivity.
Prune in early Spring before the bush breaks dormancy. Cherry buds are either vegetative or floral. Usually the end bud and thin side buds are vegetative and most of the larger buds are floral. When pruning, do not cut off tips of branches because you might be removing the vegetative buds and will have nothing to make new shoots.
Well-drained, sandy loam soil, free of perennial weeds, pH of 6.5 - 8.0, organic matter levels between 2 - 3%.
This article has more information on why your tree may not be producing.