if you conected the batery the rong way ,you might burn the internal diodes in the alternator.
if those diodes are dead or in short ,they cause problems like this that you refer.
to test this diodes you can try this simple sugestion:disconect all wires that goes to the alternator include the major one who is bolted in the back off the alternator.start the car and if the problem disapears than the alternator is dead.a new diode plate is needed.