If the alternator wasn't charging properly before, your battery voltage under load is going to measure a bit low for a while, I believe. If the new battery was damaged by the overvoltage and acid spewing you described, that may be a source of the 'low' 12 volt reading. (My battery reads about 13.5 running, 12 with engine off.) If it were steadily dropping over time, I would say you were running off the battery and the alternator still had a problem. But since it is holding at 12, and may eventually climb up a bit, the alternator is possibly doing OK. You don't have the overvoltage like you did before the brush change, so no (additional?) damage should occur to the battery. Running it for a while and checking the voltage at the battery may be in order to see what the voltage is doing. Running for a while should show if the voltage is going to decrease (running off battery?), increase (battery charging back up), or staying the same (damaged battery and/or faulty alternator?)
Also, if the battery was spewing, did the liquid get replaced? I would have the battery checked out before I popped for a new alternator.
Here is a drawing of the back of my alternator.
The bottom hex bolts 'A' and 'B' were removed to replace the reg/brush assembly. Is your alternator different?