Why deity nature appears in purity
-We hear the deities described as having bodies of light and living in an insubstantial mansion in an immaculate realm-but that is only how it appears from our point of view. The notion of being beyond corporality is an adaptation to the habitual tendency of samsaric beings(mortal who has not reach their Buddha nature), because we live in material places, in material houses and have material bodies. From the deities' point of view, there is no such concept whtasover.

logic behind spontaneity (lhundrub)

This theory stats that in the state of purity, everything in our heart, including the Buddha/deity nature, pure wisdom within our self, will appear spontaenously

Primordial purity is absence and spontaneous presence is presence; they are indivisible by law. (primordial purity without spontaneity can be seen as nihilism)

Pepperdine University

Tibetan Buddhists assume human has those following tendencies:

1.purity (kadag)

2.spontaneity (lhundrub)

3.compassion

Key theories of human nature in the perspective of Tibetan Buddhism you need to know before studying and practicing Tibetan Dzogchen

Padmasambhava, Lingpa, C., Rinpoche, T. U., Rinpoche, O. T., &amp; Kunsang, E. P. (2016). Origin: Tulku Urgyen Rinpoche. In Dzogchen deity practice: Meeting your true nature (pp. 25–30). essay, Rangjung Yeshe Pubns. 

Dzogchen Deity Practice : Meeting Your True Nature

To describe the state that all human can reach during Dzogchen. The state is described as enter a state of total emptiness. People understand and then deconstruct meaning for everything. For example, people deconstruct moral, and see there is no big or small, good or bad, pure or impure. They eliminate duality in things and just accept them as they are (suchness)

-It is part of the samadhi, a crucial mental developmental stage 

purity

spontaneity (lhundrub)

An essential mood will appear after people reach purity because of spontaneity. It is seen as part of the Buddha nature that within all sentient beings. A tendency to benefit others, to reach happiness.

"The expression of the primordially pure essence, the unconstructed nature, is naturally compassionate. These two-emptiness and compassion-are indivisible. That is the vital point"

                                  -------Tulku Urgyen Rinpoche

Compassion (thugs rje)

-In pure awareness, know as Kayas and wisdoms(related to your buddah nature), experience take place in a way that is visible yet insubstantial. This immaterial or nonphysical quality means that the experience is something you can see but not grasp, like a rainbow
(Kaya: Your metaphorical Buddha body )

-Within this  body, your realization is equal to that of sambhogakaya. All the inconceivable adornments and sceneries belonging to sambhogakaya are then as visible as rainbows in the sky. 
(sambhogakaya: body of divine enjoyment)

Learn Before

Related

Learn After