Proper rework would be remove the solder with wick, solder sucker or vacuum tool (as appropriate) and apply fresh solder or paste depending on how you chose to solder. This eliminates contaminants and the possibility the old solder having reflow issues. You would use IPA to clean both before after each step for optimal results.
Gear for you own use - if there aren't excessive contaminants and the solder looks good after inspection, generally it's "whatever gets it done". But you must use additional flux, not using it can be problematic (especially with old solder) and besides it will look crap.
Some components won't balance on soldered pads well. So preheat the board a bit with flux on the pads then use tweezers to place and hold lightly in position. You know when it's done as the solder will wick onto the legs uniformly. Some fluxes (such as tacky flux varieties) give extended work time and prevent the component from moving around, this can be advantageous as well. Another trick is to apply a little flux on the component legs.
It's not unusual to require touch ups with a soldering iron. It's debatable if it's any more efficient than removing the solder in the first place, but I'll let you discover that on your own.