I am using Turbo Tax for tax planning.
I wanted to see how the foreign income is treated, so I put the following scenario:

Ordinary US income of $10,000 and foreign income of $4,000

I see that Turbo Tax calculates AGI as $6,000. I thought "foreign income exclusion" means that you don't pay US taxes on the foreign income. I did not expect that it will reduces the US income by the foreign income amount.

Is AGI becoming $6,000 correct?

It appears that you reported $10,000 as income and then selected that out of $10,000, $4000 is foreign earned income.

Report $10000 as income. Report $4000 as income from foreign sources.

If you are a resident alien, the source of the income is irrelevent. U.S. citizens and resident aliens pay taxes on ALL world-wide income. Your AGI will be $14,000.

If you are a non-resident alien, then report ONLY the $10,000.