Is it okay to say "in their own terms"?

Solution 1:

“On someone’s terms” means according to the “terms”—stipulations or provisions—which that person sets. “We do it on my terms” means “We do it my way.” “We bought it on his terms” means “We bought it at a price he set.”

“In someone’s terms” means using the “terms”—the language, the categories, the concepts—which that person uses. “In Kant’s terms, this is the ‘categorical imperative.’”

I find it difficult to imagine a natural situation in which musicians “produce in their own terms”, or anybody else’s—perhaps Beethoven, when he abandoned allegro, andante, adagio and other Italian words in favor of metronome markings, and started using Hammerclavier instead of pianoforte?

Solution 2:

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.

Solution 3:

They indeed seem to have (re-)created music in their own terms as Bruce Eder writes in the Bee Gees biography.

Saturday Night Fever, as an album and a film, supercharged the phenomenon and broadened its audience by tens of millions, with the Bee Gees at the forefront of the music.

It was a profound moment although, ironically, there wasn't that much difference in their sound. Amid the dance numbers, the Bee Gees still did a healthy portion of romantic ballads that each offered memorable hooks. They'd simply decided, at Arif Mardin's urging, to forget the fact that they were white Englishmen and plunged into soul music, emulating, in their own terms, the funkier Philadelphia soul sounds that all three brothers knew and loved. In one fell swoop, the group had managed to meld every influence they'd ever embraced, from the Mills Brothers and the Beatles to early-'70s soul, into something of their own that was virtually irresistible. Spirits Having Flown was their crowning commercial triumph, topping 30 million in sales and yielding three more number one singles.

[emphasis mine]

Terms here seems to refer not to 'conditions', but literary terms, such as characteristic words and phrases, as the Bee Gees generally used. Did they create music using soul sounds and their usual kind of lyrics? It seems so.