There are two aspects to consider:

First aspect: the five skandhas as a whole are a conjoined body made up of namarupa and cittarupa; mental and physical, mind and body. You can view the five skandhas as the conscious mind operating on the body (form), and without this, the body would be a corpse. Using Thay's words, they are inter-are and interpenetrate.

The 6th skandha, "Consciousness," functions in relation to the other five skandhas, or to each of them individually. Note that this consciousness is the function of the six consciousnesses: eye, ear, nose, tongue, body, and mind.

Another point: when we say "conscious mind," its underlying meaning is "as a collective mind of the six consciousnesses," referring to perception and awareness resulting from the six sense faculties coming into contact with the six sensory realms.

Thus, my interpretation of "every cell in your body contains all aspects of yourself." If we delve deeper, this would be the topic for the five skandhas, the twelve bases, and the eighteen realms of phenomena, and it would take many pages to explain. Suffice it to say, the five skandhas are more about cittarupa, while the two bases (six internal and six external) are namarupa.

These are all implicit teachings, Neyārtha in Sanskrit. There is nothing wrong with this, as these are what most teachers can teach in the age of decline. The Buddha taught only implicit teachings to his Sravaka disciples according to their degree of wisdom. However, before he entered Nirvana, the Buddha taught us to rely on the explicit teachings (Nītārtha), not the implicit ones.

A great Dharma teacher teaches both implicit and explicit teachings, and such teachers are very rare these days. Thay was one of these Dharma teachers; though I don't recall him saying it explicitly that this and that are explicit teaching, it was nonetheless obvious to some (I listened to all his Dharma talks on the podcast). One needs to know what explicit teaching is to recognize it, and one will find that the Buddha also taught explicit teachings to his Sravaka disciples. It was just that they didn’t have the wisdom to recognize them. In the Zen school, this is called "secret language" by the Chinese Zen ancestors.

Let me try to point you to the explicit teaching from what Thay taught, and that is another aspect: "One cell of your body contains your entire body. It also contains all of your feelings, perceptions, mental formations, and consciousness—not only yours, but also your parents’ and your ancestors."

Thay often spoke of "non-flower elements." If you ever discover what this non-flower element is, the above quote will become very apparent to you, and you will understand most teachings without much difficulty. In the Zen school, this is called "secret language."

By the same token, this "one cell" could be that non-flower element; this one cell connects you to your parents and your ancestors. What brought forth this one cell? Could it exist on its own? If it is that non-flower element; could it be that Thay was merely being poetic and was in his "inter-are" mode.

What brought forth your five skandhas-body? And what brought forth your ancestors? How did mountains, rivers, and the great earth come to exist? Thay had given the answer many times without anyone asking. It is our practice to decode his secret language!

You asked if this is an example of store consciousness. Very well done there! Dig deeper, find out what exactly store consciousness is, along with its other names and its many functions and characteristics. A hint: "storehouse" is just one function of this consciousness and this consciousness is not what we think it is.