I would say the opposite. The trigger pulse is used to bias the left side transistor into conduction so it starts the monostable action. The diode blocks any negative voltages and is there to prevent leakage back into the trigger circuit.
When the trigger voltage (a square wave from the waveform shown) is low, that is ground or slightly negative, C1 discharges through R4. On the rising edge, as C1 charges, the current through it raises the voltage across R4 and if high enough makes the diode conduct. The waveform with positive and negative spikes is correct but it is only the positive going edges that trigger the timer.
Brian.