Several of them are actually explained in the list of Kyoukai no Kanata episodes that the OP links:
- Mirai's blood sword is carmine in color, hence "Carmine".
- The defeated youmu drops an ultramarine stone, hence "Ultramarine".
- The Hollow Shadow causes the moon to glow purple, hence "Purple Moonlight". (This is also an artistic touch we see throughout the series.)
- Mitsuki set up chartreuse lanterns in her room as a child when she couldn't go to the festival, hence "Chartreuse Light".
- Mitsuki gets splashed with pink liquid that imparts a horrible stench to her, hence "Shocking Pink".
- "White World" takes place partially in a snowy world inside Kyoukai no Kanata where Mirai battles it.
- In "Black World", a black sphere appears above the city and sucks up all the youmu.
Close inspection of the episodes might reveal more such references.
KyoAni did a similar trick with musically themed episode names in Kanon (e.g. Berceuse of a Baby Fox, A Dangerous Trio, Lieder Ohne Worte of an Elder and Younger Sister; see more). While the general music theme comes from the title of the series (which is related to the musical term canon, as in "Pachelbel's Canon", for instance), the individual titles don't have much to do with their episodes beyond the occasional shallow parallel (e.g. "A Dangerous Trio" focuses on the trio of Yuuichi, Mai, and Sayuri).