Your explanation has things I don't understand.Now follow me, using that graphic, which is correct, and I will tell you the VOLT and Amps and some time factor too.
1) Voltage went immediatly to the max of 15.9 VDC and flat lined.
2) Current draw , just like the graphic, as the intense Reversing Chemistry started to "kick the plates awake" [main reason to do this]
This graphic is NOT showing a flat lined voltage.
Number 2 problem - you can't flat line a battery that is deeply discharged with voltage. The power supply can't do it. The voltage will increase over time as the battery can accept charge. If you did try to push as much amperage into that battery to flat line at 15.0 vlts you'd fry your battery from over temperature.
So explain to me, an ignorant layman - how the front part of that graph showing oscillating voltage and current, is represented by your statement of 15.8V flat lined.
dj