Yeah, Li-xxx has a different charging schema than Ni-xx
With lithium, the charger will current-control the charge rate, initially. It will push whatever voltage is needed to provide the current that that battery can accept, until a certain voltage is achieved. (usually ~4.2V)
Once the cell voltage has reached 4.2, then the charger switches over to voltage control. It will deliver whatever (now slowly going down) current as required to maintain the 4.2 volts. Once the current has dropped to whatever the threshold for that charger / battery is, you get the green "charged" light typically. Some chargers give the green light when it switches to CV, or when the battery is ~80% charged.
The charging methodology for Lithium, is called "CC/CV" (constant current / constant voltage)
A lot of "smart" chargers for Ni-xx use something called a "delta-V peak detection" charging schema, that would seriously piss off any lithium cell, but thats outside the scope of this discussion.
4.27V is getting close enough to uncomfortable as to take notice, but if the charger is on the ball, and the cell/s are even somewhat healthy, it should be fine.