Thermoremanent magnetization data for the three-dimensional Edwards-Anderson (EA) spin glass are generated using the waiting time method as a simulational tool and interpreted using record dynamics. We verify that clusters of contiguous spins are overturned by quakes, nonequilibrium events linked to record-sized energy fluctuations, and we show that quaking is a log-Poisson process, i.e., a Poisson process whose average depends on the logarithm of the system age, counted from the initial quench. Our findings compare favorably with experimental thermoremanent magnetization findings and with the spontaneous fluctuation dynamics of the EA model. The logarithmic growth of the size of overturned clusters is related to similar experimental results and to the growing length scale of the spin-spin spatial correlation function. The analysis buttresses the applicability of the waiting time method as a simulational tool, and of record dynamics as a coarse-graining method for aging dynamics.