Warning: spoilers... lots and lots of spoilers.
Magic isn't a finite resource: it's an infinite resource, with different phases, but when the fae use any magic it often takes much longer for it to return to a usable form than it does for any other race, because they never really thought about what they were doing or spent time working out how magic really worked. They also, occasionally, poison it, always by accident, but this also has an effect on the different phases of magic.
The first phase of magic is when the magic is within the planet. With a world such as Athare it makes up the core of the planet and how much is in the core at any time depends on several things. Unsurprisingly, if someone uses their magical ability, whatever it may be, it will deplete the amount of magic within the core. Some of the abilities the fae have, such as the Blue and Yellow family's abilities to create items from magic, uses up much more magic than paper or writing magic, but all the abilities the fae have use more magic than the abilities a race such as humans would. This is part of the reason they ended up having to flee their previous home. However magical planets do have their own ways of gathering more magic to their core, in order to kept it at a safe level. Some magical planets are more sentient than others: with the more non-sentient planets it more subconcious and with the more sentient planet they conciously search out ways to increase their magic. The fae's old world was less sentient, so could do less to effect what was happening to it, and the fae were too busy burying their heads in the sand to work out how to fix the damage they had caused. Athare is much more sentient and allows the fae to work with its magic to create the new worlds, because if it hadn't then they would never have happened. This also means that the worlds created from its magic are more sentient. Part of the way Athare creates its own magic is the life clay. Almost all magic usage has waste, but the fae have never worked out a way to return the waste magic they don't use back to the world. Athare did. The life clay gathers any waste magic and makes it easier for Athare to consume, in order to keep the magic within its core at what it feels is a safe level considering the habitation of the fae. It also affected the clay, so anything made from it comes to life.
Athare permitted the use of its magic to create new worlds for one reason: it quickly came to understand the fae. For several millenia the magic within its core was barely used. Often it was used as a place to settle for a few nights before whoever it was moved on. Then the fae arrived and before the first night Athare had lost almost a fifth of the magic within its core. It is entirely possible that if the fae hadn't of made the choices they had that the magic within Athare's core wouldn't have lasted much longer than a decade. However Athare would have done everything it could to make sure that didn't happen.
The second phase of magic is when it is within the atmosphere of the world. During this phase it can't be used in any way by the fae, as they can only draw magic from the world itself, but other races can. While the Yellow family were creating races for Athare they focused on those who could use ambient magic, in part so they didn't affect the planet the same way the fae did and in part as an experiment. They believed that using ambient magic would return it to the core faster than it would if left alone. The Silver family believed there was another way to use the ambient magic and experimented with the weather to see if there was anything they could do to increase the amount of magic returning to the core. Both were, in part, right. Rain could affect the ambient magic, but this didn't always help it return to the core. Occasionally it would turn into magic rivers instead. Snow was another way of affecting it and often worked better than rain, because it allowed the magic to settle. Using ambient magic, depending on how it was used, could also help to return the magic to the core, but often ambient magic simply remained ambient magic.
Magic's third phase is when it is condensed from ambient magic into core magic. This happens in several ways, depending on the world, who lives there, and how much of an effect the world itself can have on the process. Unfortunately the fae's old world wasn't sentient enough to have any effect on the process, so it would have had to relied on evolution and there simply wasn't enough time when it realised what was happening. Athare has more options. It can rely on evolution: in some cases a species of animal will evolve into a condenser, but this is relatively rare; normally it will be a plant species that evolves, often trees, due to their connection to both ambient and core magic; and occasionally a race of people will evolve. Normal weather cycles, not those affected by the fae, also help to condense ambient magic into core magic, especially when combined with a plant species (or several, depending on the area).
Many of the newly created worlds take the time to evolve races of people and species of plants for use as condensers, because the fae have no understanding of the way the phases of magic work. If they took the time it would have been easy enough to work out, because it was the loss of several species of plant that had a huge effect on how their old world condensed ambient magic into core magic. The races that evolve as condensers can be magical or non-magical, but they often don't know how important they are to the ecosystem of the world they live on. Without someone studying magic many races also have no idea how important some of the species of plant are with keeping the amount of core magic at safe levels for the world.
Taithmarin, Aerith, and Kankirin all evolved differently, due to the way they felt about being a part of the world web. Aerith and Kankirin had no interest in being a part of the web in the same way as the other worlds, but didn't go to the extreme that Taithmarin did in making sure that the fae left and never came back. They all share magic with Athare and sibling worlds if they need it, because the magic in the web needs to stay balanced in order for all the worlds to exist.
When the fae use the magic in such a way that it is poisoned there are also species of plants that deal with this. The core of Athare does its best to make sure that it doesn't allow any poisoned magic in, because otherwise it will affect all the other worlds. If poisoned magic enters the core of any of the other planets via the world itself then they can isolate it until it's cleansed, but the magic of Athare works slightly differently, as it was Athare's magic that was used to create the other worlds and the world web, so it's permanently moving around the web.