Every treatment effect is an interaction of client, clinician, and method. It is important for you to have a clinician you feel confident with. The EMDR training is a two part basic course so that every level 1 clinician should be preparing to finish the course within a 2-4 month period. Generally it is advised that severe childhood sexual abuse only be treated by fully trained clinicians. Level 1 training is generally sufficient for single trauma, simple phobias, etc.
As far as the form of bilateral stimulation, some people can only use tones or taps instead of eye movements. If you are one of those, then certainly you must make sure to find a clinician who uses them. However, if you have no experience with using eye movements, you might want to be open and flexible to that possiblility as well.
In sum, you need to be comfortable with your clinician's ability to focus upon you and handle your problem. Having PTSD is certainly not a prerequisite for EMDR treatment. There are many applications and the experiential contributors from early childhood events can have a variety of negative effects. However, each clinician brings to the EMDR training their own vantage-point and lenses. Just remember that there are many fully trained EMDR clinicians to choose from.
Best wishes on your healing journey.