Spirits that dwell within sacred treasures called "magic lamps". It is supposed that they were formerly created at the hands of the sun god, and given to the desert kings. They normally sleep in their lamps, but when a human man rubs the lamp, they appear along with smoke. They are said to be able to grant the wishes of the one who summons them with magical power that can even be said to be almighty. These beings were originally formed from the sun god's mana. They didn't use to be monsters, but when the desert kings became monsters, they changed into monsters too, as a result of their influence.
Being sacred treasures, their very existence itself is an almighty spell formula, and they can cause all sorts of miracles using their body. However, the use of that vast power is bound by all sorts of contracts for maintenance and control, and they can't utilize their power to its maximum extent unless it's in the form of granting wishes for the one who summoned them. Additionally, the use of that power requires that an amount of mana suitable enough for the phenomenon that is to occur be poured into their body, which is a vessel that accumulates mana. Being monsters, they replenish their mana by obtaining essence, i.e., by having sex with men. In other words, it's absolutely necessary for the summoner to have sex with them in order to have his wishes granted. The bigger the wish, the more they must copulate, and the more essence he must pour inside them. For example, if one were to wish for "immortality", then he would end up having to spend the entirety of his endless life continuously pouring essence inside them, spending an eternity consumed by sex and pleasure.
Their bodies are made for the sake of having mana poured inside, so when pouring mana inside, i.e. when ejaculating inside the vagina, the pleasure the man gains is increased, and the length of the ejaculation is drawn out. This extends also to oral ejaculation and saliva swapping.
Each time a man has sex with a genie to have a wish granted, he becomes enthralled with the act of pouring mana inside her, and will end up becoming enthralled with the genie herself. Eventually, he'll wind up craving the sex with her and ejaculations necessary for granting a wish even more than his original wish. It is said that finally, his wish will be "to make her his forever."
Furthermore, the contracts binding them were weakened when they became monsters. Basically, they grant wishes to their summoner in accordance with the contracts, but if they don't like the wish, they may demand far more sex than is actually needed, and by proposing even more pleasure, they seduce the man and try to get him to spend the accumulated mana on another wish. In this manner, having become a monster makes the wild and whimsical personality which is their true nature rise to the surface, and they are not absolutely obedient to their master. In actuality, wishes cannot be granted without their consent.
Also, the magic lamps are magic items that continuously collect mana from the surroundings to maintain the genie's existence. Once they acquire a permanent source of higher quality mana, i.e. a husband, it is no longer needed. It's said that when freed from the lamp's bindings, they are also released from various contracts, and they no longer need to obey their master and grant wishes. However, once free and acting according to her own desire, a genie will love her husband, and probably try to grant her beloved husband's wishes accordingly, but the cost will be "endless sex as much as she desires" instead of "enough sex to just cover the cost of the spell".
Topic - "Genie's Magical Power"
As written in the profile, this time's update, “Genie-chan's” body is endowed with a spell formula for magic that grants wishes. Her very existence itself is a magical vessel which could be said to be almighty. There are various ways of using magic, such as chanting incantations or preparing magic circles... In other words, “spell formulas” are required. Basically, it is necessary to study them to a certain degree, memorize them, and practice. But they have the “spell formula” incorporated into their instinct itself as well as their biological structure in the first place, so just like humans innately know how to breathe, and wolves innately know how to bite their prey, they innately know how to wield magic. Races such as “owl mage”, “gazer”, etc. that are endowed with evil eye, wicked eye, and so on, and monsters such as “succubus”, etc. that are innately masters of seduction magic are the same way.
Also, there are broad categories of spells called “systems of magic”, like “necromancy”, “elemental magic”, etc. which have been mentioned in profile text. Among those, there is a system of magic called “teletomancy” which uses magic circles, altars, offerings, the performance of rituals, etc. to charge up mana and use big spells. The power Genie-chan uses is classified as “teletomancy”. You might be thinking, “Huh? There's no magic circle, nor even an altar. Besides, a ritual isn't even performed?”, but that's monster girls. Her body itself is the “altar”, and having sex with a man is used as the “ritual” for casting magic.