When I tried this, I had a most unpleasant reaction to the whole thing. I don't know why, my provider has no idea, and because of the trauma that the experience caused I never did pursue any further explanation, I just ran. For some reason, I had vivid, horrible, intense, REAL as life nightmares after my first treatment. They were, in a lot of ways, more real than reality. There are no words to describe what I saw, smelled, touched and experienced.
I wouldn't even have connected the eye movement in your post and this, except that these images have been creeping back into my dreams lately.
Not like they were then, just around the edges, hazy, but enough that they've jarred me again and are causing me some issues.
I have friends who have used EMDR and have been thrilled with the results. I just don't know why it works so well for them and it left me in far worse condition than I was in before. I was practicing witchcraft at the time, but so were some of my friends who tried it. Because of my experience, I suggest caution and much study when approaching this sort of treatment option. I suppose it's like medications, they can be very effective but can also bring side effects with them. If I had been aware of what could have happened, I probably would have tried EMDR anyhow, but at least I could have been prepared for the possibility.