That thread deals with people who don't get a salary from their LLC, and won't apply to you if you have a pass-through organization, which I believe is the much more common situation.
The tax credit certainly offsets
income from self-employment, so long as it's a pass-through organization (so not a C-corp, or otherwise set as non-passthrough). As you already know, self-employment income goes on line 12 of the 1040 (
https://www.irs.gov/pub/irs-pdf/f1040.pdf) and that ends up contributing to the AGI and therefore contributes to taxable income which then contributes to the tax on line 47, which is the number the credit is subtracted from. The credit then goes on line 54. This is all in the 8936:
https://www.irs.gov/pub/irs-pdf/f8936.pdf.
Self employment tax is line 57, which is after line 54, isn't affected by the credit. But self employment tax is not self employment income. Income is money coming in, tax is what you pay.
Like if you earn $100,000 in self-employment income as a passthrough (single member LLC, sole prop, e.g.) you will incur $15,130 or so in SE taxes (Schedule SE). $100,000 goes on Schedule C, which then goes on Line 12 of 1040. That contributes to AGI, and to taxable income, and therefore final tax (line 47). Let's say tax on $100,000 minus deductions is $8,500. You then put $7,500 on line 54, subtract it from $8,500 to get $1,000. That's your income tax liability. Then you add the $15,130 tax, which again is an outflow, not income. So you we $1,000+$15,130. This is less than the $8,500+$15,130 you'd pay without the tax.