The count rate tells you how many counts per second the photodetector of the instrument collects. It needs to be within the dynamic range of the detector for optimal results. If your sample scatters a lot of light, the instrument is going to attenuate the signal so that it still falls within that dynamic range.
The derived count rate is the count rate the instrument would measure in the absence of attenuation.
It is an indirect indication of the amount of scattering objects in your sample.
If this derived cound rate trends with time, it may indicate that some particles of your sample may be sedimenting.It could also mean that some particles are changing their shape, or aggregate in time.
In any case, what the instrument actually sees of your sample (for a backscattering setup) is the first few millimeters of your sample that are indeed on the path of the laser beam and that will scatter light to be detected. So if your sample if not homogeneous relative to the position of the laser beam, Z-average and derived count rate may change.