Yes, of course, I will be paying taxes. The company was established in June, so next April will be the first time I report and pay taxes on foreign income.
I've lived in the US for the past 15 years. Since obtaining my green card, I've spent 4 years and 1 month out of the last 5 in the US. Most years, I leave the US for at most a month. I feel that It's clear that I reside here.