It actually makes just as much sense for the populations of these creatures to be reversed, if that is what you want. If an ice creature lives at the poles, or a fire creature in the (especially volcanic) tropics, it will have a lot of ammunition to hand - but on the other hand, a fire creature has a very good natural defense against the cold, so the ability is very valuable at the poles. The ice creature has an excellent tool in the tropics - not only can it regulate its own temp easily, very few creatures would have any sort of defense against the cold in that ecosystem. So there's a good reason why a creature might have an "opposite" magic ability to its environment, that is likely what makes the ability so valuable in the first place!
Moving on, I would expect that it would take a long time, and a lot, a lot of these creatures living in high density, to even begin to dent the local temperatures and shift them. Think of air conditioning and heating, it doesn't really make a dent on the temp of the surrounding areas even if people are using them a lot (global warming being a touch more indirect) - the creatures will be using them in the open, yes, but that will also dissipate the effects more quickly... and using the ability will cost in effort and energy, so they likely won't be wasteful about it. If it is possible, I would expect them to make a local difference first (the area in which they congregate, like a city, is just a bit cooler/warmer, maybeso a few degrees), and only with high populations and many areas where they live would the surrounding temp begin to take a hit, a degree at a time.
Actually, I would think changing their surroundings in this way would be a problem for them, more than anything else, if they started in their habitats and somehow altered them to the opposite extreme (as opposed to being magically displaced into each others territory or something) - their ability would be found in the opposite environment because it's valuable there, so shifting the overall environment is likely to disrupt their living, their prey or foraging, the conditions they themselves are adapted to. They may find themselves suffering from trouble maintaining their temperatures, or finding food, as the changing temperatures devastate the original ecosystems.
The other thing is, this kind of setup would not change the nature of these areas - the global average temps are not really maintained locally through biofeedback, or anything like that, they are the results of how much sunlight and warmth comes though the atmosphere. As long as the overall planetary temp remains the same, I don't think the atmosphere or anything would be effected. So there will always be more sunlight (and radiation, and warmth) at the equator than the poles. That the populations are countering that natural resource to make the areas icy or warm, would be unnatural - it won't change the behavior of the areas, or reset them to a new equilibrium. It would actively take them continually heating/cooling their environment to the correct degree to maintain, and would reverse itself the moment they stopped.
If the heating/cooling was involuntary, then too big a population change, or actively using their powers too much, would create further temperature changes that would have have negative effects on the surrounding ecosystems that have adapted around them - again, the surrounding areas that they have to live in, where they are finding food, that they themselves are adapted to. If the change is quite gradual, it is possible that the ecosystem might adapt around them, and they maybe might survive - but any large scale use of their powers, or pushing the temp too far out of alignment with a population change or change in amount of powers used would likely devastate the local ecosystem and stave their population out.
There's also the question of where all that energy would come from, to unnaturally alter the planetary temps to such a degree - to cool or warm huge swathes of land so far out of their natural equilibrium. Maybe the species are linked, the thermal energy absorbed by one is dispersed by the other? Maybe the two areas temperatures aren't just being maintained by the two species (with the equivalent of enough energy to heat/cool the whole planet), but are somehow, for some reason, magically swapped via the species? That might almost make sense, although again, the species would need to be in equilibrium with each other for this to work and somehow be stable, and the process would need to be very slow to let their surroundings adapt (and therefore the species in question be able to continue eating)
So, given that my vote is for the populations of these creatures to have a probably negligible effect on the surrounding areas (unless they reach really dense, high-level populations)... how might you find ice at the equator and tropics at the poles, naturally. Tropics at the poles might come from volcanic activity, hot-springs all over the place, or possibly from the planet itself being very close to the sun (enough to keep even the poles warm, but them something else is cooling the equator). Ice at the equator might come from something shading the area, blocking sunlight (possibly planetary rings?), high altitudes like mountains, or the planet being really far from the sun so that even the tropics are icy (though in that case something else must be keeping the poles warm).