Jimmy Kimmel Live is not a live, spontaneous television program Wikipedia. So, my first thought was "better ask the writers of the program".
While television is usually not "real", a second thought was "there might be something here".
The comments on this question are good, and I determined to ask some questions.
There is some possibility that many Americans do not readily remember exactly how they were evaluated in school.
Older people I asked first responded "tests" when asked about evaluation in school. Younger people the same.
But further questions had the older people remembering "quiz" and "exam" also. Younger people tended to stay on "test".
Other inquiries produced an anecdote about a 15 year old girl who laughed when her father said that a "limb" had fallen on a walking path. She was sure a "limb" was an arm or leg.
There is nothing definitive in what I learned. But it may well be that English as used by Americans is evolving faster than some of us might think. It may be getting simpler. That may explain how the writer or writers of Jimmy Kimmel Live came to this attempt at humor. Maybe "exams" are not such a conscious part of some American's schooling today. Or, this whole business might be some fluke.
The answer to this question has to come from those who originated the words that motivated the question. My first thought seems validated. But, as there is little hope of getting the required information from the actual source, the continuing thoughts I had may help explain things a little.
The end answer has to involve those who created this "humor" I am sure there is no recourse to finding a definitive answer beyond the ultimate motivation for the question, those who are responsible for the program.
The term "jerked-off", meaning masturbation would have been unheard-of in Ireland (and probably Britain) in GBS's time. It seems to mean "thrown out, or discarded", so you're not far off when you say "fired":
“Jumped-up, jerked-off, orspittle-turnedout”
Jumped-up : arrogant or selfimportant.
Jerked-off : thrown out or discarded.
Orspittle-turned-out : turned away from hospitals.
https://www.pcs.org/blog/the-world-of-the-play
Best Answer
Tell us off is an American idiom. However it is much less frequently used in American literature than in British literature.
As noted by StoneyB, young children in the US would be very unlikely to use the phrase. In addition to his yell at us, young children might say