One would hope Tesco would cover any costs incurred by customers that are a direct result of this. I know banks in the past have cancelled non-arranged overdraft fees when they've screwed up, but that's easier to do as it's cancelling a charge rather than actually paying money out.
One would hope, but again time is a factor. I've had a weird "I'll be OK soon but for now I'm in trouble" situation before with Bank of Scotland back when I was a student. BOS randomly decided overnight that instead of having an agreed-upon student overdraft limit of GBP 2000 I had none whatsoever and needed to start paying them the full balance immediately. Eventually this was resolved, but for four days I was unable to pay rent or buy food. I was extremely lucky I had friends/family I could rely on in the meantime and that it was resolved so quickly, others may not be so lucky.
I am astonished how many people in this discussion are completely unaware of the idea that some people aren't as lucky as us and work paycheque-to-paycheque. I know HN/SV is a bubble, but surely we're not so out of touch with reality...