Does the corruption on Monarch and Emperor work so that someone would have to always "carry" it around, be corrupted? How would that work since only Dream and Nightmare have the ability to eat the apples, or is it different in your AU
To start with, the AU (https://chrysalisofdreams.tumblr.com) is indeed inspired by Dreamtale/ShatteredDreams but doesn't follow all the same beats/plot points/themes/etc. Same with my other Dreamtale-inspired AU (https://tippingscales.tumblr.com). There are plenty of differences and the corruption and "apple eating" bits are some of them.
The Entity, as the sentient corruption is called in Chrysalis, was imprisoned in the tree many years ago and its poisonous hatred would seep into all the fruits growing from that tree. It was forbidden to touch and/or pluck these corrupted apples.
As it mostly goes in Dreamtale-inspired AUs, the Nightmare of the bunch eats the apples and becomes corrupted. In this case, Emperor ate as many apples as he could and allowed the Entity to escape its prison and possess him... which was not intentional on Emperor's part but hey, always gotta read the fine print when making deals!
The consumption of hate-infused apples is a necessity for the Entity's corruption to take hold of someone, this is fact, buuut the Entity has its preferences too. Because the Entity is sentient, it has a personality and interests and can fall victim to temptations and similar. When Monarch ate one of the remaining hate-infused apples, the Entity was very intrigued by the development, especially because Monarch possesses a powerful positivity-infused soul (a gift from the creator of the 'prison' tree to fight back against the Entity), and wouldn't it be great to extinguish that powerful thing, or corrupt it to grow even more powerful? Yes, it would!
So the Entity switched hosts and while it hasn't won full control over Monarch's empowered soul yet, it is content with possessing him because of the added bonuses, like being able to enter other universes that have positivity in them.
You can read more about the AU's summarized backstory here.