That is strange, usually adding new drives to a system may cause the boot order to need adjusting, but if you set it correctly it should work. Also, if a device is say first in the boot order, but is not bootable (no MBR and OS) it should be skipped.
When you say the PC tries to boot from the empty drives, can you explain that in more detail?
When you installed your OS, your main SSD was the only drive in the PC, true or false?
Both of the new drives are just that, new, never used, and empty or now with just data and non-OS files, correct?
Did you try clearing the CMOS/BIOS, with all the drives connected, then reset any BIOS settings you use and set the correct boot order? Some BIOS have not only a main boot order, but boot priority lists for types of devices, like drives or network devices. Did you check those and set them correctly?
My board has a boot order selection of Disabled, meaning no device. Can you set that as the second, etc boot device, to force only one?
Is your DVD drive in the boot order?