The "standard" idiomatic meaning of on one's own terms is in accordance with one's wishes : in one's own way. In that link, Merriam-Webster's example is he prefers to live on his own terms.
"In one's own terms" isn't such an established idiom, but it's certainly not uncommon. There's a degree of semantic overlap anyway, but it seems to me about half the instances linked to there basically have the above meaning. The rest have the more literal sense we normally see rendered as "In one's own words" (using the words and phrasings one is most familiar with).
My advice would be to stick to "on your own terms" when you mean something akin to done in line with the terms and conditions you have decided upon, and use "in your own words" for the sense of described using your own natural language.
In short, "they can produce music on their own terms" would normally mean they make music the way they want, but "they can produce music in their own terms" could easily be taken to mean they make what they call music, but other people might just call it noise.