You know that Intel Matrix Storage software is installed because it's available from the Start menu. I use it and it automatically detects external eSATA hard disks.
Before connecting your external drive via eSATA, do you disconnect the USB cable from the drive enclosure?
Yes, the usb is disconnected before the esata cable is connected. This is done with both the PC and hard drive off.
The software I have installed is called Intel Rapid Storage Technology. I went to the Intel site and downloaded the Matrix software. It failed with message that my system didn't meet the minimum requirements. My cpu is an i7-3770k.