Unless you are expressly told otherwise, all deadlines are based on the flight's originally scheduled departure time, not modifications made later.

We also do not know OP's departure airport or departure time and that may also affect whether check-in counters are even staffed. Last flight out of a smaller station may mean that the check-in person migrates to the gate to handle the departure and, in a delay, there is no counter because the deadline has passed.

Details may matter.