If I understood you correctly your power supply and PCI-e power cable is similar to my own. One end of the cable has a single connector that is plugged to the PCI-e connection on the power supply. The other end of the power cable is split into 2 PCI-e connectors that are plugged into one video card that requires 2 connections. That is perfectly normal. It should be okay.
Your video card came with a power cable adapter that has two 4 pin molex connectors on one end and a 6 pin or 6+2 pin connector on the other end. Normally that adapter is used when a power supply does not have a second PCI-e connection designed for use with a second video card for Crossfire or SLI mode. Although it would work, use of the adapter cable for a system with...