I used Turbotax Premier to file my taxes. I had some capital gains from sales of stocks and ESPP. Were the taxes I owe on the gains automatically deducted from my refund?

Yes, all your income and withholdings are combined. After all the calculations, if you paid in too much, you get a refund. Your withholding also goes to potentially cover the amount on which you had no tax withheld.

Yes .... all your income is reported on the one tax return and the taxes owed are paid using the withholdings and what is left over will be the refund of the excess payments.