When adjusting a turnbuckle on any flight control, we usually use a wrench and turn the hex shaped section of the rod end inserted into the turnbuckle barrel. That flight cable from the turnbuckle is connected to a stationary non rotating component, but when we turn it aren't we just twisting it at that point, which causes stress loads on it.
Yes the cables can be twisted if proper care is not administered during tightening. There are tools that allow for tightening the buckle while keeping both ends untwisted. From this article:
Cable tensions are adjusted by twisting the turnbuckles that connect different sections of cable together. It’s a simple system, but you need to hold each cable end stable while turning the turnbuckle in order to avoid putting twisting stress on the cable itself. If you work alone, you may want to invest in a cable turnbuckle tool that holds both cable ends stable while you twist the turnbuckle barrel.
One bolt has a left-hand thread and the other with a right-hand thread:
If you lock both wires and turn the common nut (barrel) no twist is added to the wires. This is the proper way to proceed. With someone to help, this can be done easily, but you may use a tool to lock the ends and turn the barrel.