Yes, it could only be voltage regulator, it supplies the voltage to the rotor in the alternator, and thats what sets the output voltage
Do a quick test first, Key off
Unplug the 3 wire connector on alternator
Test battery voltage, says its 12.8volts
Test voltage on the Yellow wire on the connector, should be exactly the same, 12.8v, if not then that wire has a poor connection and would cause the higher voltage
Voltage regulator works by "electromotive force", easiest way to understand it is "pushback force"
Just after starting battery is drained, so it will take all the voltage it can get, for a minute or two then it starts to "pushback" it doesn't want so much voltage, so voltage regulator lower voltage(to rotor)
When you turn on the lights or blower fan to HIGH, pushback in the system drops, so voltage regulator sends more voltage until lights are powered up and fan is spinning at high RPMs.
The Yellow wire is voltage regulators connection to the "system", so if it has corrosion on its connections then voltage regulator is getting less pushback so it cranks up voltage
Bad battery can do the same, it never gets fully recharged, it wants more voltage all the time, which is bad for it, lol, I know your battery is new just mentioning it for future reference