If you want to take the best care of your batteries:
Get the charging specs for your exact battery model/technology, they vary
Program the absorption and float voltages according to the battery specs. Really sophisticated Chargers also have minimum times at each stage which help extend battery life. With batteries that cost $6K a modern high end charger may be in order. It’s constant current in bulk charging until the absorption voltage is met and the minimum time is met, absorption voltage/time, then float voltage indefinitely, unless the charger current output is exceeded and the battery voltage drops, then back up to bulk/absorption voltage
Install the temp probe option for your charger, the correct charging voltages vary with temperature quite a bit at the extremes. A good charger will also shut down on a high temp fault so one shorted cell does not result in a total loss
Both overcharging and under charging reduce battery life
Some batteries recommend a routine equalization algorithm for maximum life which is a higher than normal charge or a pulsing high charge for a certain interval
So this charger shuts off at some point and does not leave a float voltage on the batteries (cuts out)? I would again, refer to the battery manufacturer for their ideal charging specs/routine.