Consider the following two sentences:
People in North America are predominantly English speakers.
People in North America are dominantly English speakers.
Merriam-Webster defines predominantly as "for the most part; mainly"; and while it doesn't directly define dominantly, the definition for dominant is "commanding, controlling, or prevailing over all others". Therefore, I would take dominantly to mean "in a commanding or controlling manner".
What I don't understand is how adding the prefix pre- changes the meaning of dominantly to the aforementioned definition.