@pk
We need to know what is Mark's home country, what kind of visa he will have, his dates for entering and leaving the US, what kind of job (wages, official or under the table, or self-employment) and maybe a few other details.
In general:
If an alien (not a US citizen or green card holder) is temporarily in the US and does not pass the substantial presence test, they file a form 1040-NR to report and pay US tax on US-sourced income only (such as wages from working inside the US.). Note this is legal or illegal employment -- the IRS does not inform to immigration services but they want their tax money if Mark works, whether or not he works legally.
If the person does pass the substantial presence test, they are a US person for tax purposes and they pay US income tax on all their world-wide income. They may be able to claim a deduction or credit if they pay tax on the same income in their home country. The substantial presence test is a bit more complicated than just "183 days". See link.
https://www.irs.gov/individuals/international-taxpayers/substantial-presence-test
If the person has US-source income (regardless of whether or not they are a resident alien or non-resident alien), they must generally pay into the social security and medicare system, either via social security and medicare tax withholding on wages, or via self-employment tax on self-employment income.
If they work overseas, they do not need to pay into the US social security or medicare system (this is also true of US persons working overseas).
If a US person works overseas more than 330 days, they may be able to exclude the foreign income from US tax. That does not apply to a non-resident or resident alien working IN the US. They either pay tax on their US income, or all their income, depending on the substantial presence test. But they may be able to claim a credit or deduction if they also pay tax on the same income overseas.
If a person owes US tax, and does not have withholding (because they are self-employed or working under the table) they need to make estimated tax payments to the IRS. If they don't make estimated payments, they can be assessed a penalty even if they pay in full when they file their return. If they overpay the estimate, they get the difference back as a tax refund. However, the penalty for not making estimated payments is not too bad, it's about 1.5% per month of what was owed.
