Being authentic to your characters do you write as they speak or do you write as you speak?

There is nothing wrong with the grammar or punctuation or syntax and pacing. I had a professional editor from Book Baby edit the first 100 pages. The first two people who read it on Goodreads and my professional reviewers gave me a 4 to 5 star. In the first three chapters, my characters are Lebanese from Beirut speaking English they live in Beirut that is the way they speak English I am authentic to my characters?