If any of my officers had told me to pick up their dry cleaning, or to walk their dog, I would be obligated to tell them no, and that it was an unlawful order. Officers cannot order enlisted personnel to do personal errands for them.
A quick example..........................an officer could tell me to go out and wash the Navy owned vehicle and clean it up, and would be perfectly legal to do so, since he's ordering me to take care of Navy equipment. He could also tell me to go outside and pick up the trash around the MEPS building, as that is also military property I'm being ordered to take care of.
If he tells me to wash his personal vehicle, or police the trash around his own personal house? That is an illegal order, because he can't use military personnel for private business.
Pompeo has no right to tell his underlings to pick up his dry cleaning or walk his dog. Those aren't government things, and he cannot tell government employees to do his personal stuff.