It all depends 😉 If your short fringe is on an item that is just lying around on a flat surface, like a table runner, hem stitching is enough. If your hemstitch is for a linen scarf, linen isn’t happy being twisted into a fringe and it’s a non slippery yarn, you’ll also be fine. However, if you have woven a scarf with silk, bamboo or another slippery yarn, then twisting your fringe gives you a secure and elegant beginning and end to your masterpiece! Also, keep in mind that a loose fringe will get frayed more easily if it’s an item that is washed frequently. What have you woven???

Sounds like you have a well thought out plan in place! It could be that either the fringes that became untwisted either didn’t have good knots securing the fringes and/or the fringes weren’t twisted enough.