Whether you get an additional refund or owe tax from adding a second job depends on the amount of income and withholding you are adding.
Without seeing your return, it's not possible to tell.
Adding income may put you in a higher tax bracket. It may also lower or eliminate some credits such as the Earned Income Tax Credit or education credit.
Withholding on each job is figured as if that is your total income, unless you made the multiple job adjustment on your W-4. If you had, say a part-time job, generally almost no tax would be withheld because the income would be so low. But if added to a full-time job, the tax rate would be much higher and you would owe on the total.
It's also possible the W-4 on one of your jobs was filled out wrong.
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