Why it is likely that you owe taxes or get smaller refund when you change job? Our tax system is such that the more you earn, the higher rate at which you pay tax. Let us use a example to illustrate the concept.
Suppose your annual pay is 20,000, and the tax rate is 10% for the first 10,000, and 15% for the next 10,000, then the total tax you need to pay for the year is:
tax = 10% * 10,000 + 15% * 10,000 = 2,500
The average rate is:
average = 2,500 / 20,000 = 12.5%
To have a uniform stream of income, the tax is withheld at this average rate. Suppose you sign up a job at the beginning of the year, and you quit the job after the half of the year, the tax you have paid is:
tax1 = 12.5% * 10,000 = 1250
Suppose you found another job immediately with the same pay, the new company should have continued with the same rate of tax withholding, but in reality they don’t. They assume 10,000 is all you will earn for the year without asking nor caring how much you have earned in your previous job, therefore they will withhold 10% of the tax for you. Thus the tax you paid for the second job is:
tax2 = 10% * 10,000 = 1,000
In the year end when you file your tax return, IRS does not care you have worked with one or two companies. As previously calculated, the tax you should pay is 2,500 for the 20,000 total income. Comparing what you have paid for the two jobs, you have a shortage of 250.
You can imagine either that the first income pushes the second income to high bracket, or that the second income pushes the first income to higher bracket. It does not matter, they are different interpretations for the same math formula.