Just from a cannon perspective, I don't know if it really needs it's own race. I mean it's your own custom scenario, so you can do whatever you want, but typically a cambion is half-demon while a tiefling is simply anything less than half-demon.
Basically, when a demon has a kid with a mortal (making a half-demon child) it is called a cambion. However, if the demon blood is diluted further, such as a demons grandchild, or great×17 grandchild, it is called a tiefling.
Again, you can alter this depending on the specifics of your particular world. For example in 5th edition tiefling traits tend to be dominant, so the child of a tiefling would likely be a tiefling. However, I like playing in a world where tiefling traits can go dormant for generations, so a family could suddenly give birth to a tiefling because someone 8 generations ago was a demon.
I thought about this a lot given the history of the race, but in the 5e PHB it specifies a human bloodline. And I really wanted to make this race for my world as you say, so there it is!