So, how do we avoid being "seen" as we write?
Read, read, read (educate ourselves to recognize what good writing looks like). Remember to be subtle (treat your readers as "smart" - don't hit them over the head with obvious details). Practice good grammar and mechanics (those are the basics every writer should know).
And, in the end, just use your writers' instinct. Listen to your gut as you write. Let your voice come through. As long as it's natural, as long as you're being truthful with the emotion in the scene, you're less likely to be "seen" writing.