Yes. Deductions will be made with after-tax dollars which means the STD/LTD benefits will not be taxable. Deductions are taken in advance just as they are for other benefits, such as medical and dental.
Please note that the long term disability insurance FAQs are for state employees only. The state of Tennessee does not offer long term disability insurance to higher education employees. If you are a higher education employee, direct questions on LTD to your agency benefits coordinator.