Yeah, that was a bit of an odd way to approach that. I remember in an old EU game or book they had the Jedi broken down into different categories, with each color representing a different one. Have they done anything like that in the new canon?
The way it's supposed to work is that natural living kyber crystals are usually clear (like the one on Jyn's necklace.) It only takes on a colour when it is awoken; for Jedi that process is about establishing a sympathetic bond with the living crystal, for the Sith it's very much an act of domination. That process is euphemistically referred to as "bleeding the crystal" as it always produces a red crystal (you can even see one amongst Luke's collection of artefacts on Ahch-To; a relic of the ancient Jedi Crusades.)
As to a specific meaning for the non-red colours; with the exception that white crystals appear to be what results when a red is purified, so far there doesn't seem to be any. Or at least none that can be so narrowly defined and that's probably for the best.
It seems to just be an expression of the bond between a specific Jedi and a specific crystal, at a specific time. Note that Ezra's kyber changed from blue to green when he re-bonded it to make his second sabre, and Anakin managed to change Ahsoka's green crystals blue when he refurbished them.
It's also worth keeping in mind that the supposed "purpose" of the colours in Legends mostly comes from the games, which means it has more to do with serving the game's mechanic (character class systems, specifically) than any actual lore, so I wouldn't put much stock in any of it. Same with the "lightsaber forms" (because that's not how actual sword fighting works) and the idea of "force powers" (because that's not how the force works.)
On top of that, it's best to remember that the real-world reason for all the colours is rather more arbitrary. In ANH's pre-production the idea was that ALL the blades would just be red (because: laser swords!) Then when they decided to try capturing the effect in-camera with the retroreflective tape that dictated that they'd all be white . . . then when that didn't work very well, it went back to red and a rotoscoping process. Then while editing the Vader/Kenobi duel it became clear they needed to be different colours to more easily differentiate them in some of the tighter shots, so they made Obi-Wan's & Luke's blue.
Roll onto RotJ and again, the plan was the make Luke's blade blue . . . but the thing about the Sarlacc fight is that the sky that's in the background of almost every shot, is that's it's very very blue, which for the photochemical processes of the time meant that the blue blade wasn't registering very well, so they switched it to green.
Purple famously came about because Sam Jackson asked for it. Lucas initially said no, but later relented. The darksaber was originally just going to be a vibroblade, but Lucas didn't like the idea that any kind of normal sword could resist a lightsaber, so they came up with the idea of it being some ancient Jedi relic that the Mandalorians stole (whether the crystal is black or white is a matter of debate; personally I say it's white but have a rather unique emitter to give it that flattened shape.) The yellow blades first cropped up with the Temple Guards, with the idea being that those weapons were antiques that were issued to the guard from the armoury, not their personal weapons.
