My understanding of Intel RST is that it increases boot speeds by writing the startup instructions to a hidden partition. This benefits HDDs a lot, but SSDs not so much.
Your R/W speeds are almost exactly on spec. The Asmedia ports if they are true SATA III ports should not be a factor. The limitation with non-native (Intel) SATA III is use as a boot drive. If you use non-native SATA III to boot there is the need to load the hardware drivers for the non-native SATA III which slows down the boot. But speed, after the driver load should be similar.