The Self Employment Tax isn't impacted by your standard deduction or exemptions. The self-employment tax is calculated based on net income from self-employment (Schedule C/ 1040, line 12). The tax carries to the end of your tax return, after your regular tax is calculated. The standard deduction or itemized deductions, nonrefundable tax credits, and exemptions reduce any regular income tax you might pay. They don't impact the SE tax. Only business expenses on the Schedule C can reduce your SE tax.
You can owe SE tax even if you owe no income tax, just like you pay Social Security and Medicare taxes through a job and don't get them back no matter how little you make.
The only things that are applied against SE tax are federal tax payments and refundable tax credits, such as the Earned Income Credit.
If you made $13k in net self-employed income, you are paying little or no personal income tax. But you are paying a decent amount of SE tax.
