As far as I know, there is no recognition of immunity indicating that employees of ministers are not obliged to testify before a committee. In my opinion, it is rather a reason given to you, when you are presented with this important principle of ministerial responsibility that makes ministers accountable to Parliament. Since employees are accountable to the minister, they put forward this argument.
If the matter is brought forward, it is up to the committee and ultimately the House to determine what course of action to take.