Thank you very much, Allan.
I got and installed the latest version of "Intel RST" from Intel's support site (version 13.2.4.1000) and it did the job! I was able to disable integrated disk caches of the physical drives. It was confirmed by "Intel SSD Toolbox" (now the value of "Drive Details, Word 85, Bit 5 - Volatile Write Cache Enabled" is reported as equal to 0) and the write performance measured by CrystalDiskMark is normal, low .
For some reason the support site of Asus does not offer the version 13.2, but the version 12.8, which appears to be quite old. I had searched Intel's support site, but in wrong download category, so I did not find the newer version. Thanks to you, Allan, I was able to got the newer version and soled my problem.
Regards,
Dimitar