start signal is sent, timing starts immediately, start signal is later lost but timing continues.
At the end of t1 gate signal is received, timing is paused as long as gate signal is present.
gate signal is removed and t2 represents additional timing period.
This is a model of "on delay operation" what they didn't show is actual set time and maybe could have done a little better job representing that somehow, it is in this example at the end of t2 time period.
They could have possibly shown several instances of gate signal in there and set time may have occurred at t10 or something or even between t5 and t6.
If gate signal is received after set time is up, it doesn't really do anything as output relay is already on. need a reset signal or loss of power to reset things.
If you have gate signal when start is applied - start is initiated but timing won't happen until gate signal is removed.