What does this sentence from the Tempest mean?

According to the footnotes in a version of The Tempest edited by Horace Howard Furness, and published in 1892:

"He who 'deals in the command,' or, in other words, executes the office of another, is termed his lieutenant or viceregent, and is usually authorised and commissioned to act by his superior. Prospero therefore, I think, means to say that Sycorax could control the moon and act as her viceregent, without being commissioned, authorised or empowered by her so to do." (his emphasis)

What this would suggest is that "deal in her command", means to control the moon, or use the power of the moon, while "her power" is the moon's power/authority (the moon is given feminine grammatical gender), which Sycorax does not need to control tides etc.