Here:
http://www.ssac.com/timerscat/Sect5DOM.pdf the TRM series on PDF page 4.
If the Coil is activated when the pump turns on, that's the activation signal. If the timer completes, it would turn on the RESET coil of the relay.
Each coil of a latching relay is held magnetically therefore a continuous energizing and a pulse will activate it.
DC latching relays are easier to understand because the polarity of the coil determines whether the contact bar is pushed toward or away from say the NO contacts. The single coil latching relay uses a change of polarity to latch and unlatch the contact.
So, once this relay is latched, if the system looses power, the relay stays in its previous position. Once it's latched, then the motor contactor coil would be unable to get power.
The SET coil would just be activated with a pushbutton.
The total # of components is possibly 3.
A small DC power supply might make sourceing the delay on break relay easier.
Power failures will not cause any issues with operation.
Additional options is the use of "alarm contacts" or "indicator lamps". 24 VDC is common for industrial controls.
To me a DPDT latching relay would make sense. One contact for "contactor disable" and the other for "Indicator or alarm".
Now does it make sense?