The voltage read-out on the 1093DBD can be different at times from battery voltage. I have a 1093DBD too. Yes it does temperature compensation which affects the voltages.
It is normal for battery voltage to keep rising during the Absorption Stage. It is hard to measure what the charger's "own" voltage is when they are connected. They are at either end of the same wires, so the voltage difference seen is affected by voltage drop
With an adjustable voltage charger you can "set" the Vabs voltage, and battery voltage will rise to that. When they are the same voltages, no current, and you are done. But long before that, amps will taper from the constant amps stage.
Just what the SOC is when amps start to taper depends on the charging rate (charger amps wrt battery capacity in AH.) Vectors are a little different by having that "trip" occur at 13.9v.