From what you've quoted of Ott, it sounds like this "Ubiquity* Doctrine" holds that Christ's human nature is His divine nature. This is the heresy of monophysitism,** which says that Christ only has one nature, not both human and divine natures.
*(ubi- = Latin for "where" or "in what place")
**(mono- = one; phys- = nature)
It is not necessary, for explaining how Christ can be substantially present under the Eucharistic species in multiple locations around the world, to think that Christ's human and divine natures are the same. In fact, even some saints have bilocated, and they certainly are not God.
To understand this, we need to first understand the distinction between
- accidents ("properties").
The substance of something is its essence, the answer to the question "What/who is it?" Accidents ("properties") inhere in a substance; they are not essential to it, but they cannot exist without it.* For example, my substance is myself, what makes me to be what I am (my particular body and soul). My hair, for example, is an accident, a quality of myself; I am still myself regardless whether I have hair or not, if it is long or short, etc. Another accident of myself is my location. I am still the same substance regardless where I am; viz., it's not essential to myself to be located in a particular place. My size is another accident of myself; I have always been myself even when I was as small as a fetus in my mother's womb or as large as a grown adult.
*(except in transubstantiation, where God miraculously maintains the existence of the accidents of bread and wine without their inhering in the substance of bread and wine, which is replaced by the substance of Christ Himself; cf. the Catechism of the Council of Trent, ch. The Holy Eucharist, § "Three Mysteries Of The Eucharist")
With this understanding, you can follow St. Thomas Aquinas's reasoning when he answers the question "Whether the whole Christ is contained under this sacrament?," Summa Theologica III q. 76 a. 1 ad 3:
Some terminology he uses:
"dimensive quantity" = e.g., length, breadth, width;
"by way of substance" (per modum substantiae) = "substantially";
the adverb "locally" (localiter) = "place-ly" or "in the manner of a place (locus)"
As has been already stated (Question , Article 5*), after the consecration of the bread into the body of Christ, or of the wine into His blood, the accidents of both [the bread & wine] remain. From which it is evident that the dimensions of the bread or wine are not changed into the dimensions of the body of Christ, but substance into substance. And so the substance of Christ's body or blood is under this sacrament by the power of the sacrament, but not the dimensions of Christ's body or blood. Hence it is clear that the body of Christ is in this sacrament, and not by way of quantity. But the proper totality of substance is contained indifferently in a small or large quantity; as the whole nature of air in a great or small amount of air, and the whole nature of a man in a big or small individual. Wherefore, after the consecration, the whole substance of Christ's body and blood is contained in this sacrament, just as the whole substance of the bread and wine was contained there before the consecration.
*"Whether the accidents of the bread and wine remain in this sacrament after the change [effected by consecration]?"
Finally, we can understand his answer to what appears to be your question: "Whether Christ's body is in this sacrament as in a place?," in Summa Theologica III q. 76 a. 5 c.:
As stated above [what I quoted above], Christ's body is in this sacrament not after the proper manner of dimensive quantity, but rather after the manner of substance. But every body occupying a place is in the place according to the manner of dimensive quantity, namely, inasmuch as it is commensurate with the place according to its dimensive quantity. Hence it remains that Christ's body is not in this sacrament as in a place, but after the manner of substance, that is to say, in that way in which substance is contained by dimensions; because the substance of Christ's body succeeds the substance of bread in this sacrament: hence as the substance of bread was not locally under its dimensions, but after the manner of substance, so neither is the substance of Christ's body. Nevertheless the substance of Christ's body is not the subject of those dimensions, as was the substance of the bread: and therefore the substance of the bread was there locally by reason of its dimensions, because it was compared with that place through the medium of its own dimensions; but the substance of Christ's body is compared with that place through the medium of foreign dimensions, so that, on the contrary, the proper dimensions of Christ's body are compared with that place through the medium of substance; which is contrary to the notion of a located body.
Hence in no way is Christ's body locally in this sacrament.
The reason this may seem obscure is because the question of place or location* is an immensely deep physics concept, like time or infinity. See Catholic physicist and historian of physics Pierre Duhem's magisterial, 10 volume work in the history of medieval physics:
Partially translated in:
The medieval physicists' penetrating disputations on place, in part to understand transubstantiation more deeply, laid the foundations for modern physics, as I discuss on History of Science SE.
*(In Latin there are several words for these related concepts: ubi, locus, positio, situs, etc.)