Hi Georgina,
You wrote, "Even if the communication happens instantaneously, there will be a delay between that observed event."
No. "Instantaneous" means that the two events are observed to be simultaneous. It doesn't happen, because all physical influences are communicated at less than the speed of light, making all events observer-dependent; i.e., there is some spacetime separation between any two events, such that observers in each inertial frame interpret the time of each event incident differently, and each interpretation is valid. There is no lapsed time for simultaneous events, just as there is no lapsed time between the endpoints of a beam of light.
Tom