Just as their name implies, a locking tuner locks the string in place with a clamp, preventing the need for winding during restringing and enhancing the tuning stability of the instrument. This makes them a desirable upgrade for guitarists as you can make a drastic change to the amount of time it takes to change strings.
Whilst locking tuners do provide an upgrade to tuning stability, your tuners aren’t the typical cause of instability. It’s far more likely that the nut is the issue, with the way the string sits in the nut being the usual culprit when it comes to tuning instability.