In order to make all those animals intelligent, tool-users, you'd have to modify them to the point where they would only look superficially similar to what they once were. Think about how large the skulls (and thus heads) of say a fox would have to be in order to house a brain capable of human-like intelligence. And what of the arms/paws? You need dextrous hands, fingers and especially opposable thumbs in order to manipulate tools effectively. So while there is no reason why you couldn't modify the fox genome to meet your requirements, the end result wouldn't be as fox-like as you might want.
But beyond that, as far as how long it would take, that merely depends on whether or not the gene-manipulators know what they're doing. If the hyper-intelligent "magical" creatures that overthrew humanity have a very good grasp of genetics and furthermore know exactly what precise changes they want to make, then it could take very little time (less than a century).
Gene manipulationm as you call it, doesn't take time in itself, it's rather knowing what genes to manipulate that's difficult and takes time.
At the moment we humans have severe holes in our understanding of genetics, we don't currently create [GMOs][1] with a set plan in mind, instead we experiment and see what changed genes express what characteristics and eventually we manage to bring about positive traits.
But this doesn't have to be the case, we're already attempting to create more or less complete models of gene interactions in species with primitive genomes ([for example yeast][2]). It is likely that within the next few decades we'll have succeeded to do such not only for the latter but perhaps for all species including humans.
So to finish, it really depends how good geneticists your "magical" creatures are. If they have an advanced knowledge base then it could take very little time, if their knowledge base is poor it could take centuries for a single species, that with millions of failed attempts (that last part isn't pretty to think about). [1]: https://en.wikipedia.org/wiki/Genetically_modified_organism [2]: https://www.ncbi.nlm.nih.gov/pubmed/17449820