I believe that they should have stopped right there at the question and admit that as humans these concepts cannot be fathomed. An existence that does not exist in time and space is beyond our comprehension and that is all we can say about it. If we don't understand its existence how can we ask how it occupies more than one space? In fact the limitations that we face in understanding Him underline His uniqueness and are a cornerstone of real monotheism.
As Rambam says:
"Consider well that the expression" dwelling over it," is used by them, and not" dwelling in it." The latter expression would have implied that God occupies a place or is a power in the sphere, as was in fact believed by the Sabeans, who held that God was the soul of the sphere. By saying" dwelling over it," they indicated that God was separate from the sphere, and was not a power in it.
Clearly God is not in the universe but separate from it and the Rabbis were very exact in their language when trying to depict how God has an impact on it, they use a term that connotes Him being outside of it, lest we think of Him as a natural component of the world.
Addressing the word place - Makom - as it relates to God, Rambam in Moreh 1:8 states:
"In the verse," Blessed be the glory of the Lord from His place" (mekomo) (Ezek. iii. 12), makom has this figurative meaning,(" position," or degree," as regards the perfection of man in certain things) and the verse may be paraphrased" Blessed be the Lord according to the exalted nature of His existence," and wherever makom is applied to God, it expresses the same idea, namely, the distinguished position of His existence, to which nothing is equal or comparable, as will be shown below.
The word Makom instead of implying space when it is used with God it reflects a status that we confer to Him in our mind when we meditate about Him, His uniqueness. Once we have accepted that whenever there is a connotation of location when talking about God it means a hierarchical position Rambam in Moreh 1:19 deals with Melo Kol Ho'oretz Kevodo -
"In this sense it is said" The whole earth is full (melo) of his glory" (Isa. vi. 4)," All the earth gives evidence of his perfection," i.e. leads to a knowledge of it. Thus also" The glory of the Lord filled (malei) the tabernacle" (Exod. xl. 34): and, in fact, every application of the word to God must be interpreted in this manner; and not that He has a body occupying space."
The word "Melo" translated as full, means that the world when looked upon by us, in its magnificience, every detail of it, conveys a sense of God's perfection.
To me this understanding of theses concepts is so elevating and thought provoking that I don't understand why reduce God to an imaginary presence everywhere through Tzimtzum to accomodate a literal reading. Tzimtzum is not understood by us either so what have we gained? Even if the original thinkers who came up with the idea had something in mind that could be seen as not pantheist, their followers have certainly distorted it and turned it into a Meshichist nonsense. It is the story of Nadav and Avihu who went further than was permitted and, in spite of their greatness, "Bikrovai Ikadesh", they were wrong and misguided.
This reinforces and explains the importance Rambam placed on understanding our limitations.