Okay, let's start by looking at the poker hands
View attachment 954038
(Since we play with Jokers, there's actually a 5 of a kind as well, but the principle applies).
A tier1 gem (like fire1, poison1, etc) fits into a One Pair, or anything higher (so you could put at fire1 in a Royal Flush slot, it just wouldn't be a very good use of the slot). A tier2 gem (fire2, poison2) fits into a two pairs (and anything above), etc.
You can only get access to tier1-8 through monster drops and shops; the Tier9 (True Flawless Gems) are given out at story points.
As you advance through the story, there are moments when MC's power levels go through a quantum jump (so he gets much stronger). That's represented by being able to slot the tiers 1 lower (so now a fire2 can fit into a One Pair, a fire3 into two pairs).
Hope that helps clear it up.