The SCSI ID, whether the drive is terminated or not, and whether term power is on or off is set by jumpers on the hard drive.
You must be sure both drives are not configured for the same SCSI ID, and also not for the SCSI ID of the computer itself.
If the adaptor you have is to connect a 68 pin device to a 50 pin bus, you will lose the added performance of the hard drive with this arrangement. For this arrangement to work, you must turn OFF termination on the first drive in the chain, and ON for the last drive in the chain. unless the internal SCSI cable has a built in terminator at the end, in which case termination on all connected drives should be OFF.
The problem may be that the adaptor is actually to connect a 50 pin device to a 68 pin bus, and I don't think this will work at all. 68 pin devices are usually backward compatible with a 50 pin bus, but only with the correct adaptor, and then the increase in speed of the device is lost.
Better to get a PCI SCSI host adaptor. They are not expensive on E-bay. Make sure the one you buy has an internal connector. I think some had external connectors only. ATTO made nice ones.