Yes, 2019 TurboTax handles the catch-up properly. Make sure you've entered the HSA owner's birthdate correctly (some date prior to 1965). If you are filing jointly with your spouse the catch-up appears on Form 8889 line 7, otherwise it's included in the amount on line 3.
Also make sure that you have installed the latest update to 2019 TurboTax. The initial release on the CD was still using 2018 contribution limits.