Try not to over tighten the belt.
Are you "making the face" when you load your belt tension?
I know it sounds rediculous, however many people here have improperly over tightened and ruined the alternator bearings.
Lighten up a bit, make certain there's no squeal and check it again, please?
Your alternator should not be re-charging your battery.
Your battery charger should have brought your battery up above 12v before you installed anything.
4 wire alternators need to see 12v or they do NOT charge anything.
Always best to make certain the battery is fully capable and full charge before testing.