I have seen many errors on the Military website and when I contacted them, I was told they are not tax advisors and the information posted is merely that, informational, even if it is wrong. I believe this is where that oxymoron, "Military Intelligence" is applicable.

As sjrcpa said, a servicemember does not pay State tax if he is not stationed in his home State.

Each State is different in how they tax Military pay. Ohio, for example, has a special IT- 4 Withholding form for the military which excludes any State or School District tax withholding when stationed outside of Ohio. 

Review the State regulations for where your clients call home.