I don't remember any of those with the standard Telechron movement shut off after one hour when the function switch is set in the "auto" or alarm mode.
The only delayed off is the sleep function. You're dealing with a device that was built 60+ years ago. It's only a 12 hour clock as well! :scratch2:

I was aware that it's a 12 hour movement, most electromechanical movements (Except some of the flip-dial movements like the Sony's and Sankyos were 12 hour movements). But I thought that the radio was supposed to shut itself off after an hour when set to alarm/radio mode.

On a Zenith clock radio I have I had to adjust the alarm hand on the shaft to get the alarm to go off at the correct time.

Yes, When I took the radio apart to work on it, I had to remove the clock mechanism to clean and lube it and when I did that the hands popped off the dial on me and I couldn't remember what position the hands were in before they came off, so I had to put them on the best I could remember that they were on there as, but I have a feeling that the alam pointer/hour hand and alarm wheel wasn't put on correctly, but I have no idea how you can tell where to position the alarm hand in order to make sure the alarm wheel and pointer are lined up properly.
Any tips on how to reinstall the hands on the alarm clock mechanism on this thing so that its actually installed correctly?

One thing I used to do is IIRC set the alarm by setting the time backwards...It would the clock hands/gearing would hook the alarm hand/gearing and it would allow the alarm to be set to exactly the time the hands were set to....Then the clock hand would have to be reset to the correct time by moving them in the opposite direction that I used to hook/set the alarm...That seemed to be the easiest way to get a really accurate alarm time set.

OK, well I think I tried that but I don't know how well that worked with my situation seeing as I was working with the clock mechanism that had the hands completely removed from the clock dial so when I ran the clock mechanism backwards to latch it into the alarm triggering mechanism I couldn't tell where the hands were or should of been, so like I said I kind of guessed on mine in reference to where I had previously had the alarm set to but I'm thinking that the guess wasn't very accurate or at least the way I positioned the hands wasn't very accurate (especially the alarm set disc in reference to the alarm pointer on the back side of the hour hand).

OK Weird issue with my Clock mechanism on my Radio that just suddenly cropped up.
The Alarm Buzzer will go off at the set time but without the alarm buzzer being turned on, what's weird is that it didn't always do this, it just randomly started doing this one evening while I was reading in bed and all of the sudden my buzzer starts going off and I looked at the clock and I saw that it wasn't even set to go off (it wasn't turned on).
The only way to shut it off was to "turn it on" or pull the knob out to the on position and then wait a little bit until the buzzer sounds again and then push the knob back in and it turns it off.

Any ideas what might be causing the alarm clock mechanism of this radio to do this weird thing its doing?