I once tried to charge one of my batteries on one of the multi-chargers that a friend had. You need to push the button on the battery to initiate the charge. Autel battery charged faster on the multi than the stock charger by about 5min.
When I went to use that battery a bit later in the day, the XSP returned a error of unknown battery. Had to shut down the battery & reboot the battery in the XSP. The XSP then recognized the battery after that and flew as expected without issue. Scared the hell out of me at the time, but it really hasn't been an issue since. My friend said not to worry about the unrecognized battery error as it wont hurt anything, he gets them all the time on P3 & simple reboot does the trick. That is my experience with this so far.
I do not think the 0.6v makes much of a difference. a 4S battery is still a 4S battery. The only difference could be the tolerance levels of the smart chip in the battery. If the charging voltage was too high, the smart chip would shut down the charging. If the battery was too hot during cycle, the smart chip would shut down the charging.