Difference between Time up and time over

My try:

Let's say you have 60 seconds to answer a question. You say "time's over" after the 60 seconds, maybe at the 61st or 62nd. You say "time's up" just as the bell rings, that is at the 60th second.

 

"Time's up" (The time is up.) means there is no more time for the task at hand.
"Time's over", at least to my AmE ear, means nothing at all, nor does "time over" unless the words are functionally separated, as in "I spent a lot of time  |  over at a friend's today".

CJ

I don't know if this collocation is used in ESL/EFL locations other than Japan, but in Japan, it's really common. It's very likely a construction that was put in a textbook at one time and like so many other mistaken phrases, was believed to be the normal one for English.

As others have related, it is not natural English at all. These fossilized "errors" are extremely.difficult to eradicate. You can tell teachers time after time that the phrase is, "Time's up" and in the very next class, out will come, "Time's over".