You should not be albe to turn the alternator pulley by hand with the belt on it. If you can make the belt slip by hand, it will slip when running. Either the belt is too loose, or it is not a good belt.
Some brands of belts will grip better than others.
I doubt you have a tensioner. If you are not sure about the proper tension to set your belt, drop by a GM dealer and ask them to show you.
We have 1974, 1977, 1981, 1984 year model chevy pickups on our farm, ALL have had problems with belt slipping.
My old 84 pickup was one of the worst offenders and had a pretty good wrap on the belt, meaning the belt only ran the alternator on that model, but still slipped unless very tight, had a good pulley, and the belt was less than two years old, (Gates).
The older models the belt ran the alternator, then went over the smog pump pulley, so the alternator only had about a quarter of the pulley in contact with the belt! They would slip very easily.
Some alternators don't come with a pulley, and you have to re-use yours. Others come with a new pulley. I don't know if any come with a used pulley on them but it's possible.
Examine the pulley belt groove closely and see if the sides are flat.
Check my web page for First Gen Camaro suspension info:
David's Motorsports page
First Gen Suspension Page
67 RS 327 original owner. 69 Camaro Vintage Racer, 65 Lola T-70 Chev SB Can-Am Vintage Racer