That all looks correct. You do owe $4,367.
In rough numbers, the tax you have to pay on the additional $12,000 of self-employment income is 24% income tax plus an effective rate of about 12.4% self-employment tax, which comes to total additional tax of about $4,367. So you have to pay back the $3,974 refund that you received, plus $393 to pay the total additional tax of $4,367.
If you had included the $12,000 in your original tax return you would have had a payment due of $393 on the original return instead of a refund of $3,974. That's probably where the $393 came from that you saw in a summary somewhere in TurboTax. That was before taking into consideration that you already received a $3,974 refund that you weren't really entitled to.
Amended returns can be confusing.
