Idiot lights came on dim, Alternator not charging

[kkamen]

Almost all the idiots were lit dimly when my girlfriend brought the car home. Checked around. Bad ground and alternator was the gossip. Ok. Put in new alternator, lights went out, yet no 13.8-14. Rev engine a little for a little and boom hello voltage. Turn off same thing consistently. So question;
Should the voltage be 13.8-14.1 immediately? I would think.? If so I got a bad alternator from autozone. NEXT at first I only had 13.2 when it finally came up, remember initially dim idiot lights, that went away as soon as we changed alternator but after cleaning all connections real good I got 14.1, now when I turn key no more idiot light initially then go out like they used too. No bad connections no forgotten wires. Checked coolant sensor by shorting all good, window washer lever sensor lights light just not the intialazation of the left lamps, brake etc. ABS, SRS and check come on when key first turned then out after start. They all used to light. I don't know the norm at this point?

summary: 1. should alternator voltage be 13.8-14.1 upon start up immediately?
2. Why would pre start up light check crap out after cleaning all connections and getting great ground and voltage. Just can't win...