It has often been reported that spontaneous REM is generated with other types of bilateral movement such as handtaps or tones. It is quite possible, therefore, that the same processes apply. However, also remember that dual attention, bilateral movement, rhythmical movement, etc. are all common denominators of all three types of stimulation. It may be that in waking state there are simply more choices for stimulation of the necessary physiological mechanisms than are available in the sleep state when only the eye movements are possible. On the other hand, the entire REM hypothesis may prove to be incorrect and merely an interesting analogue. Only time will tell.
Comparable effects have been reported with all three forms of stimulation depending upon the individual client. Some clients cannot track at all, others have no response to taps and excellent reponses to audio, etc. However, you might want to remind your client that it is not necessary, or possible, to hold the image steady when the eye movements begin. The trouble they are reporting might be based upon a misunderstanding. If they think they are supposed to hold the image steady during the eye movement they will find it impossible, and therefore believe they are failing in their task. The idea is "just let whatever happens, happen" during the sets of stimulation--in whatever form.