I am going to go out on limb here and postulate that if you drew an org chart foe the entire executive branch, diligently following the chain of command for each agency, sub dept, department and so on until you get to the top, it would be Trump in that top mpst box. That implies "working for" to me but that doesn't really matter as long as every executive branch employee is accountable to an individual boss who is responsible for exercising managerial oversight.

But such an org chart would be incorrect, because every employee isn't accountable solely to an individual boss (leading up to the President). Congress also exercises oversight, and Congress also tells all those employees what to do.

The federal government is not analogous to a private business. In a private business, management makes all the decisions - and all power to decide matters for the company is vested (ultimately) in the CEO. The federal government doesn't work that way. We have divided government, and many (if not most) decisions for the government are made outside of the Executive altogether through Congress' laws and budgets. You can (and often do) have a situation where the Congress and the President are diametrically opposed to each other and neither can do anything to get rid of the other, which rarely happens in a private company.

It is a fundamental error to think about the federal government as if it were like a private company with an org chart. That's not how it's structured.