You do not get a separate payment for a dependent. The credit for your dependents was subtracted from the total amount of tax that you owed, so you owed less because of the dependents.
Look at your Form 1040. The credit for other dependents is on Form 1040 line 19. It's not necessarily $500 for each dependent. The amount depends on your total tax.
Also look at the Dependents section in the middle of the first page of your Form 1040. The last column on the right is for the credit for other dependents. If the box in that column is checked for each dependent, then you got the credit.
