There are 18650 batteries with protection circuit and without. It's basically over-charge, under-charge and high temperature protection. More info. When charging any battery higher voltage means faster charge and it's usually not a problem. What is a problem is heat generated. If you can't dissipate heat fast enough, then you have a potential problem. Slower charging is always safer.

And all charging processes are adaptive voltage to a degree. Say you are charging 18650. Your charger will start with target voltage and constant current at 500mA, and watch the voltage in the battery raise. Once voltage reaches target it will remain constant but charge current will slowly drop. Once there's no current going in, battery is full at that voltage level. Some chargers will push more current in, some will try higher voltage initially then switch to target voltage. Higher current can be a problem due to chemistry stability and heat but higher voltage should generally be safe. You can even revive some of the old batteries that no longer have any charge by shocking them with higher voltage shortly.

Also, good charger matters a lot.