Breaker or wiring problem

The two hot wires are 180 out of phase so when you go across them you get 240V. Maybe you are checking one of the lines to ground instead of to the other hot line.

Nun, check voltage at the input to the timer, then its output

I wonder however whether single- or two-phase . If two, things get more complicated. And are you measuring across the supposedly 220-v terminals or are you holding your black prod instead at ground (edited to add) as supposed by Eng

If single- then you might be in real trouble depending on exactly where you're holding that black probe; so please don't electrocute yourself before additional careful measurement, for instance what you're assuming neutral maybe really isn't

I'm going to assume, but it is not clear, that the wiring goes straight from the breaker to the timer ? It is unlikely for a fault to drop the voltage to exactly half, so I expect you have 120V deliberately for the pump . Does the pump have a data plate saying what voltage it is ? Does the timer ?