The main difference between red and black is that you can boot off of devices connected to the red ports, but you cannot boot off of devices connected to the black ports. So, if there is a device you may wish to use as a boot device (i.e. your main HDD and perhaps a DVD or CD drive) connect it to the red ports. If it is just a data device that you will NOT use to boot your machine, you can use either a red or black port.
I would probably connect all SATA devices to the Intel ports, and only use the JMicron controller for the PATA drive.
EDIT: Sorry, just to be clear: the six SATA connectors located towards the front of the Mobo (SATA1 through SATA6) are ALL for the onboard Intel controller. The ONLY difference between them is that the two black connectors (Sata3 and Sata4) are "slave" and the other four connectors are "master". The SATA connector for the JMicron controller is towards the rear of the Mobo and is labelled SATA_RAID. In my system I have all SATA drives connected to the 6 Intel Sata ports.
It is somewhat unlikely that plugging a drive into a red or black port will make the system unstable, I don't think. I am not sure why you are assuming that this is the cause of the problem.