Check Charging System

My wife's 2004 Expedition 4.6L had a check charging system warning and
the battery light was on. I checked the alternator and it was only putting out
14.0 vdc. We replaced the alternator and my son said he confirmed the
battery was charging however when my wife went out to start it up the next
morning the battery was dead. The battery had been fully charged and the
car was driven about 12 miles on the bad alternator. Then the alternator was
fixed and driven back about 18 miles. The check charging system is still on,
does this error have to be manually cleared after repair or once the
alternator was installed should that have cleared the warning if the battery
was correctly charging? I am sorry for being wordy or stupid but I am  just
not a mechanic.