This is very clearly an outlier one that seems to have been exacerbated by the seasonal adjustment factors. If you look at the non-seasonally adjusted data, usually September is a month where 20-24 year olds leave their jobs, but for the first time, there was actually a slight increase in employment:
It could very well be that as parents have less money to help pay for school, college kids are having to increasingly chip in on tuition, taking part time jobs instead of just focusing on their studies (or just extending their summer employment longer to keep the cash flowing). The way that seasonal adjustment factors work is that if you were expecting a decline and instead you get an increase, your adjustments are going to make that increase much much larger.
One thing to note is that this kind of job increase is certainly not a sign of an improving economy, it's more of a sign of financial strain on those who normally don't have to work to get by.
What about the other 58%? It looks like just noise. Take a look at this graph of what happens when you subtract the establishment survey job increase number from the household survey one:
They often differ and sometimes can even be contradictory. If you subtract out the 20-24 year old seasonally adjusted job gain, the difference is in the range it is normally.
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