The more income you have, the more tax you pay. Your tax is not calculated separately for each W-2. The amount due is based on your total income and the total amount of tax that you had withheld from your pay during the year. So the refund or payment due that is shown in TurboTax doesn't really mean anything until you have entered all your W-2s and other income. When you enter another W-2, it adds to both your total income and the amount of tax that was withheld. Depending on the amounts, that can make your refund go higher or lower than it was with only some (or one) of your W-2s.
When you enter the first W-2, the refund that is shown takes into account your personal exemptions and the standard deduction, which significantly reduce your taxable income. But you don't get more exemptions or deductions when you enter another W-2. All the exemptions and deductions are subtracted from the income on the first W-2 that you enter. So when you enter another W-2, the full amount of income is added to your taxable income.
