Reman'd alternators have gotten progressively worse and worse, while their marketing saying how great they are has goten more and more generous to themselves.
Lifetime warranty means one gets to spend a lifetime replacing them over and over until they get one that was actually rebuilt by somebody not completely inept.
They ONLY replace that which was obviously failed, like perhaps one of the two bearings, and put it in a new shiny box.
If a Diode or 2 has failed, it will let alternating current into the DC wiring, and all sorts of weird crap can happen. and yes it can do this and still make 2/3 of its rated output, which can be more than enough to maintain expected voltages when the battery is fully charged and loads are only headlights.
A super hot pulley is an obvious sign that either the pulleys are badly misaligned, or perhaps a 3/8" belt is bottoming out in a 1/2 inch pulley, or the front bearing was bad and not replaced.
I bought a New nippondenso clone alternator from Autozone. Made in Malasia. rated 50 amps idle 120 amps max. When hot it is abuot 32 amps max at idle and can't produce more than 109 amps, so even the new ones are not built as good as OEM quality, but can be more than good enough, especially if one does not have the ability or desire to measure its output at different rpm with loads capable of fully fielding the rotor.
Here is a long involved article about mounting and aligning alternators. I recently found my stock original alternator location had the pulley 6mm out of parallel alignment.
Now I have that AND the ND alternator within 0.5mm.https://marinehowto.com/marine-alternator-installation-tips-tricks/
Using the info in that link, and a good straight edge i also found my power steering pulley well out of parallel alignment. V belts do seem remarkably tolerant of misalignment, and Ignorance of the rather profound misalignment on my 318, was certainly blissful, But I am happy to have all the pulleys much better aligned, and I am sure my belts and pulleys are much happier too now.