Yes. Per the IRS:
Individuals, including sole proprietors, partners, and S corporation shareholders, generally have to make estimated tax payments if they expect to owe tax of $1,000 or more when their return is filed.
Based on your initial scenario, you would probably not need to pay estimated taxes. However, if you underestimate your Tik Tok income you may face a penalty for underpayment. It would be more conservative to believe that you may indeed owe estimated taxes.
You will use Form 1040-ES to calculate your estimated taxes which you can pay by mail, online, by phone or via a mobile app.
For more information, please see the IRS website: Estimated Taxes
You don't report the income, you just pay estimated taxes. You may need to use the income to calculate the estimated tax, but you don't report the income to the IRS.
If your withholding from any regular jobs is large enough to cover the tax from a side business, you don't need to make special payments. For example, the tax on your side business could be between $1300 and $1700 depending on your other income. If you normally get a $2000 refund, that means you are overpaying into the system by $2000, which is enough to cover the side gig (you would get a refund of $300 to $700 instead). But if you still like the large refund, you have make payments into the system.