The old job was taking out taxes for the old job tax rate. The new job has a higher tax rate, you just did not have enough withheld from the old job.
You were making $x and paying y% in taxes. Now, you are making more money and paying z% in taxes.. If you have a second job, those will never withhold enough and you have to have more taken at your main job. On the W4, there is a box where you can withhold additional money, if needed.
Congratulations on the new job! The taxes should be better when it is a full year. You may want to check the W4 calculator in the program to be sure. It is in the Other Tax Situations tab.
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