The kit locking nuts are normally OK but do need to be used with a (not-included) string retainer bar (a few $ on eBay or Amazon) to pull the strings down onto the block at the neck side so the clamps only have to hold the strings tight and not pull them down as well. Also makes the initial tuning before locking work so clamping retains the tuning. You don't then have to take several turns of the fine tuners just to get back to where you were, allowing more range in the tuners for normal operation. Illustration here: https://hazeguitars.com/blog/locking...bar-adjustment

Otherwise a FR is very similar to a Fender Strat trem in operation, though you have a lot more up and down movement available. The bridge plate need to be adjusted to be parallel to the body, or else it won't return to tune accurately. And it helps to wedge the block in place when putting strings on and when tuning initially before locking, so that when you adjust the rear springs to get the plate flat, the strings will be at the right tension. They'll need fully stretched-in first, so don't lock the nut straight away. Take some time to stretch the strings and retune until the tuning is stable, then lock the nut.

If the springs are too loose to begin with, the bridge can angle right forwards under string tension and the springs then can't be tightened enough to bring the bridge flat due to geometry issues, so put a decent amount of spring tension on the trem springs to start with before removing your blocking wedge.