With the Thomastik strings, and any other classical strings, after you cut the end, if you light a match, and ever so slightly burn the end so that the inner nylon fibers form a ball, and just touch it with something flat like the side of a knife or flat screwdriver blade, it will force the plastic to curl back OVER the edges of the metal windings. Thus capturing the windings and preventing future unraveling.
Also, as an alternative, after you cut the string, you can paint a few drops of clear nail polish over the last 5mm of the string end, which also will stop the windings from coming apart. the downside to this is the smell of the nail polish (which is gone once it cures and dries) and also the time you need to wait for it to dry (maybe 30 mins?).
I have done both of the above many MANY times, each with good success to prevent wound strings from coming apart after cutting.
Also, with the Thomastik strings, if you want to cut off the red silk overwrap part at the bridge end, you can also do either of the above to prevent the string from unwinding.
I have also tried the precision cutters, but have been unlucky to still have a problem, and thus found the above additional solutions to work well for me.
It just feels a bit funny as a man buying clear nail polish in the store, and the teenage girl behind the counter always giggles at me when I go to pay for it. It's not like I'm buying PINK nail polish but she laughs any way.