You are correct, but he can direct the Guard, after the governor activates them. And they are in constant contact with each other.A Mayor can not call out the National Guard.
The Governor can.
Here's a report on one of his speeches taken out of context:
And, as the National Guard has been tapped elsewhere, he reminded residents that the military has not been officially mobilized in the city. He said, when that that time comes, he will let residents know.