No it doesn't work that way. You have to file all your W2s on the same tax return. You get the refund or a tax due on your total income, not for each one. Did you already file the first W2 without the other 2?
You only get one refund or tax due for all your income combined. The Refund Monitors won't be right until you have entered all your income. So don't look at it until you are done.
That's common. It just looks that way because you put them in as separate W2s and saw the tax due change in between them. If it all was on one W2 you would get the same answer. And each job was withholding like it was your only job.
Because you only get one standard deduction no matter how many W2s you put in. Turbo Tax starts out by giving you the Standard Deduction. You entered more income when you entered the second W2 but you didn't enter more deductions. And each job only withheld taxes like it was your only job for the year. You might want to adjust your withholding. Also as you add more income you might not be getting as many credits as before like the EIC credit. And it was probably giving you the EIC credit until you went over.
See, https://ttlc.intuit.com/community/refunds/help/why-did-my-refund-drop-when-i-entered-a-second-w-2/00...
