It's not clear whether you owe taxes with the W-2 omitted, or after you add it. Did you file an amended return to add the missing W-2? What is "it" that says you owe tax?
But in any case, you don't automatically get a refund for each W-2. Whether you owe or get a refund depends on your total tax for the year, for all jobs put together, and the total amount that you had withheld from your pay, for all jobs put together. If the total amount that you had withheld is more than your total tax, you get a refund of the excess that you paid. If the total amount that you had withheld is less than your total tax, you have to pay the difference.
Adding another W-2 changes the totals. It could go either way. It could change from a refund to a payment due, or from a payment due to a refund. If you got a refund on your original tax return, with one W-2 omitted, and then filed an amended return, the amended return takes into consideration the refund that you got on the original return. If the refund on the original return was more than you should have gotten, based on the correct totals for the year, then you have to pay some of it back.
