You can owe taxes in the US after paying taxes in the host country. But the US encourages that you pay tax first in the host country and take a credit from US tax obligations.
The US has a worldwide taxation policy for its citizens and residents; it does not matter where you earned your money or where you are living. You cannot escape US taxation unless you renounce your citizenship or residency.
You never pay taxes in two countries. America encourages people to pay tax in their host country and then take a foreign tax credit from their US tax obligation. I have done it multiple times in my life. IRS Form 1116 is for foreign tax credits.