I agree that it does seem like a large swing between a refund and balance due, but in order to understand exactly what happened, you need to look at the overall tax return and not just the 1099-MISC income.
When you entered your Form 1099-MISC income, there were more changes than just addiing the self-employment tax. You increased your taxable income, took a deduction for 1/2 of the self-employment tax, and added the self-employment tax. This also changed your Adjusted Gross Income (AGI), which may affect certain credits that could be on your return. Increasing your income could reduce any Earned Income Tax Credit (EITC) that may have been included. Bottom line, the effect on your overall return is more complicated than just the increase due to the self-employment tax.
If you really want to understand what happened, you should compare your Form 1040 before and after the change of adding the Form 1099-MISC. You can still do this without deleting the work you did to add the Form 1099-MISC, just change the amount of income shown to $1 instead of $3625.
Then, use the steps in the following TurboTax article for how to preview your Form 1040 using TurboTax Online:
How do I preview my TurboTax Online return?
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