I would expect that any state's DOH would be dealing with local issues, like licensing of facilities, licensing of healthcare workers, etc.
Something like the containment and treatment of a specific, very lethal virus like this, which involves taking a great deal of care with exposure of the healthcare providers, would naturally be directly overseen by the CDC.
Surely the CDC would communicate with other gov't health agencies and drug companies on matters like caring for such a virus, and share data, procedures, etc.. Not to mention the fact that the CDC has presumably worked with this virus in a lab setting before? I wouldn't expect a state or local DOH agency to have either experience or even the authority to oversee that aspect.
Your same question could be directed at the City of Dallas DOH. Would you expect them to be all over this issue and issuing directives? If not City of Dallas, why the State of TX? This is a virus with clearly national implications. To have each state (or city) DOH determine their own ways of dealing with it seems like a recipe for disaster, given how difficult it is to treat someone with this disease. The biggest issue is the side effects (projectile vomiting, bad diarrhea, external bleeding) which make this particular difficult to treat. With other lethal virus/diseases like AIDS, etc., the patient (for the most part) isn't a time bomb that could easily spread their bodily fluids with the lethal virus onto you or your protective clothing without much warning.