Alright, here is a long line of technical analysis followed by gradparantal ranting: first things first: yes a trigger job will void warranty: if sent in for work (to HK) they will replace all modified parts at your expense to bring back to spec for continuation of warranty, choose your gunsmith wisely.
The hammer following the slide = You just fired a round at the target, the slide cycles as usual, upon the slide closing (going into battery) the hammer going back to half-cocked or hammer hitting the firing pin!! The hammer is supposed to be cocked. At this point the disconnector will still have the trigger bar disengaged (until you release trigger to allow reset) otherwise if the hammer missed the catch (due to "adjusted" sear/catch spring) it could fall on the firing pin. Freeze frame: at this point you need to ask yourself if your lazy gunsmith disabled the firing pin block (some do!!), if he did you could have an accidental discharge or have uncontrollable firing of your gun.
Firing after battery means a gun fired a second round after the slide closed (like in the above scenario) and you only pulled the trigger once, not good. It may/will fire a 2nd round before you have your sights back on target, at this point a nearby LEO will be curious as to how you have a legal post '86 machine pistol (which doesnt practically exist)
I may sound hard-lined about this but it applied to all makes and models: gunsmithing is serious business. The above scenario has happened to some, one poor sap actually did some time in "club fed" due to poor smith work (on an ar) while the feds sorted out what happened, he was still responsible for what his weapon did. Heres the point: poor smith work = non-functioning firearms. If you look for 1911 trigger job complaints you will find similar issues = not for combat and may not be safe
If you cannot find a good, reputable gunsmith then do the smart thing: only use genuine HK parts to improve your trigger feel: match hammer, match hammer spring etc.
It must be understood that a good trigger helps with accuracy but range time is essential to learning the feel of a trigger for real world use, regardless of how good or bad. Quality range time will outweigh a "bad" trigger, but HK does not really sell guns with bad triggers. Think Im joking? Get some quality range time then try an USP trigger under stress. this is the part where I am supposed to recommend safe dry firing to get the feel for your trigger, but that requires a whole 'nother safety lecture......Have fun and stay safe