So, if I'm understanding how to use the Mutant Fire Cat cards (cards that turn a Fire Cat into another school's cat) correctly, you can only use them if 1) you have a fire cat card in your hand as well as the mutant card, and 2) you can only use the mutant card if your primary school is the same as the mutation.
From my Experience as I dabbled in the mutate of cards for a bit. It goes like this, for an example:
You need to use this card and any other mutate card on a card that is not a treasure card (or a yellow card) so if you want to convert a fire cat to a thunder cat you need to have a non treasure card in your deck to cast the mutate. in which this case is the Fire Cat.
So this means if you already decided on your primary and secondary school, and neither your primary or secondary was Fire School, you have to make your primary or secondary School Fire to get non yellow Fire cats, to use Transmute on it.
The same goes for all of the other transmute cards, you have to be in that particular school of study to get Non treasure cards ( yellow card).
Also I did the change secondary over to the particular class of the card or cards you want to mutate over. and convert back to your original secondary. If you make, say three lighting elves, from life elves, and convert back to your original secondary, and Life is not your Primary or secondary school you will only have those three mutate elves to use, and that is it, until you get more regular life elves, and more mutates for them.
Also if you stick points into, for an Example: Life School to learn Life Elf, and convert back to your other Primary/Secondary that is not Life School, the points get erased and you will not get anymore Non Treasure Life Elf cards. or regular life elf cards.