No Turbotax does not pay your tax. if you e-filed and selected direct debit, the IRS will use the routing and account numbers and date specified to take the funds from the account. actual withdrawal might be a few days later but as long as you specified a date on or before 4/15 you're safe
this info only appears on the info worksheet - nowhere on the 1040. there is no acknowledgment of this and you should check to make sure your e-filed return gets accepted.
if by chance you mailed your return, making payment is your responsibility. file form follow Turbotax's instructions
