Hi, I am working on my 2021 tax return with turbo tax. Do I have to pay the taxes owed immediately when I file this way?

Taxes owed on the 2021 tax return are already late.  You should pay the taxes owed as soon as possible since penalties and interest will continue to accrue until the taxes are paid.

You can mail the tax payment with the Form 1040-V payment voucher.  Or you can go to the IRS payment website to pay electronically - https://www.irs.gov/payments

You can pay anytime you want but interest will continue to accrue. 

If you owe tax due for 2021, and have not paid yet, you are going to owe late penalties and interest along with the amount of tax due shown on your Form 1040.   The sooner you pay ---the better.  TurboTax will not calculate the interest or penalty---the IRS will bill you when they receive your return and your payment for the amount shown on your tax return.

If you do not owe or are getting a refund, there is no penalty for filing after the deadline.

 If you have federal tax due you can pay by mailing your payment with the 1040V voucher, (which has the address printed on it, having the payment taken out of a designated bank account, or you can pay directly on the IRS website. 

https://www.irs.gov/payments

https://ttlc.intuit.com/community/tax-payments/help/how-can-i-pay-my-federal-taxes/00/26212

https://ttlc.intuit.com/community/tax-payments/help/how-do-i-pay-my-irs-tax-due-with-a-check-or-money-order/00/26403 

To apply for a payment plan with the IRS

Apply Online for a Payment Plan

You must pay your state tax due using the state’s preferred method of receiving payment.  For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.

https://ttlc.intuit.com/questions/1900884-what-are-my-options-for-getting-my-state-refund-or-for-paying-any-state-taxes-i-owe

https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue