Coincidence means synchronous detection.
Since the Geiger triggers from a partial discharge of ionization from high energy X-ray or gamma waves (and other wavelengths like neutron bursts), a residual charge is stored and accumulates. The difference level between the “activation threshold and the sum of the residual charge and incoming excitation pulse level determines if it will fire a pulse or not. A large input pulse may be coincident but smaller ones will be stochastic or random in a limited range just as recall how quasi random the static sounds on a Geiger meter. The repetition rate of quasi random spaced pulses increases with energy level if the radiation pulses.
So this is a way to quantize the energy level in addition to the repetition rate of this “partial discharge” (PD)type counter.
The same is true for leaky grids that have PD stochastic internal discharges due to contamination storing voltage on lower capacitance contaminants than the adjacent molecules of higher Dk insulation. These tend to be quasi random but since excited by sinusoid all HV grid voltages on oil or plastic insulation , they tend to occur on the rising cave edge just before or at the peak voltage with a wide distribution of phase. Yet gamma rays are are not sinusoidally excited and caused by galactic events or nuclear material. The contaminants being lower Dk and thus capacitance charge up faster and exceed breakdown voltage and then discharge locally and ionize and detonate that tiny particle.
The coincidence detector would be some inclusive AND logic within a certain time interval (tbd) using a 1-shot from multiple detectors.