The number of events do not scale in the same way. Suppose we expect on average n=RΔt events in time Δt. The same rate applies to each Δt so for ΔT=mΔt the number expected is N=mn=mRΔt=RΔT. The rate, R, is independent of the size of the period of time involved.
The number of earthquakes of different magnitude which occur in a given period of time can be treated as an urn problem.