Batteries usually charge at up to 14.4V.
They are usually 12.67V fully charged.
Your reading of 13V and above is "surface charge" which can take up to a day to dissipate.
Usually after stopping charging at (say) 14.4V, the battery drops quickly to around 13.5-13.7V, and eventually to ~12.7V.
A quick drop to 12.7V may indicate aged batteries. eg a high internal resistance that discharges the surface charge quicker, or a general lack of capacity or collapsed cells etc.
FYI - If using voltage to measure battery condition after charging, for new car batteries, 10 or more minutes with headlights on may be recommended to remove surface charge, else leave disconnected (ie, OC = Open Circuit) for 24 hours.
A fully charged battery is 12.6 - 12.7V OC (no load). (In theory it's 12.67V @ 25 degrees C.)
A fully discharged battery usually about 1V less, but can vary from ~11.3V to 11.8V.
For cranking batteries, the usual recommendation is not to discharge more than 20% - ie, ~0.2V down from its full voltage, so maybe down to ~12.5V or ~12.3V.
For deep-cycle batteries, the recommendation is no more that 50% discharge, so maybe down to ~12.2V or ~11.9V depending on the battery. (The same recommendation applies to deep-cycles that specify 80% discharge.)
BTW - the OC voltage drop is linear between its fully charged and fully flat voltages wrt its remaining capacity.
OC voltages are not to be confused with "loaded" voltages. Internal resistance means a voltage drop at the terminals, and the internal resistance increases as the battery discharges.
Hence it is common to see battery a "end voltage" specified at lower a voltage - eg, 10.7V @ 20A, or 11.3V @ 10A, but that might correspond to an OC voltage of 12.0V (remove the load and measure).
Batteries will also self-recover after removing loads (unless they are in really bad condition).
I'd suggest your batteries were damaged after their flattening. The cells probably haven't collapsed since it recovered to 12.5V, but they may be heavily sulfated.
But they will require
battery maintenance - ie, boost and equalisation charging above the normal maximum of 14.4V, and probably using 20A or more.
The sooner the better because the sulfation that forms when not fully charged goes hard after about a week and is then impossible else difficult to remove - the loss of capacity is then essentially permanent.
Though batteries can often recover from over-discharge (flattening), the older they are, the less they recover.
And any battery should be recharged ASAP after a discharge.
You could have a look at Bill Darden's
batteryfaq.org - namely the top link to
Car and Deep Cycle Battery Frequently Asked Questions (FAQ) (or even download its zip file as per instructions under the last
section link
Battery.Zip).
Also, I hope you are disconnecting your batteries from each other when not in use. (Or as often as possible when not required or not being charged.)
If one is worse than the other (a lower voltage after recharging),
do not reconnect them to each other unless you're milking the last out of them - the bad one will damage or destroy the good or better one.
And if you replace one, replace
both!