I was on Obamacare for 5 months last year then I started receiving employer provided health insurance. It looks like I have to pay back some of the tax credits I received. Is that correct?
Yes, you will need to repay some of the Advance Premium Tax Credit.
Obamacare looks at your actual income for the entire year in determining whether you paid the right amount for your Marketplace health insurance.
This is a problem many people experience. When you have little income or become unemployed during the year, you have no way of predicting what your actual income will be. If you get that great job, or get married during the year, you may end up paying back some of the APTC, in spite of your best prediction of your annual income when you bought the insurance.