I want to make sure I understand your question. Your wife is an employee (W-2) of (possibly)a local government organization that does not pay into the Federal Social Security or Medicare systems?
When you first enter your personal information as Married Filing Joint, Turbo Tax is working behind the scene, and already has calculated the allowed standard deduction and exemption amounts based on your personal information.
When you next entered your wages (without your wife's wages) Turbo Tax then begins calculating your "refund" based on the information entered so far which does not include your wife's income, but is including the standard deduction and exemption amounts for Two individuals filing jointly. This initial refund amount showing is a "projected" refund and is based on incomplete information.
Next, when you add her income, your refund goes down because turbo tax had already used the standard deduction and exemption amounts in the running calculation of your refund. Your wife not paying into social security/medicare is not causing your refund to decrease.