At this point in sci-fi and fantasy cinema history, I don't know how commonplace it was for made-up languages to actually be spoken on set. As a comparison, Greedo's dialog and voice in Star Wars were formulated and dubbed in after filming.
For TMP, I think it was easier to come up with the Klingon dialog to be spoken on set because there were only a few very, very short lines in that scene. James Doohan came up with the Klingon words, and Mark Lenard spoke them. But the dialog on Vulcan was more extensive. According to behind-the-scenes anecdotes, the Vulcan scene was intended to be in English in the first place, but then, after the fact, production staff did not like the way the scene played/sounded in English, so Roddenberry had the idea to dub in a new language for the Vulcans, seeing as how they already had the Klingons speaking their own language. So UCLA linguistics professor Hartmut Scharfe (who also developed dialog for the Klingon scene, but his work ended up not being used there) came up with alien-sounding lines to match up with the movements of the actors' mouths. Some accounts claim that Doohan came up with the Vulcan dialog, but that seems unlikely.
And then the same thing was done for the Vulcan dialog in TWOK. But this time it was a different linguist named Marc Okrand who was involved. Okrand's story is that Spock and Saavik's dialog was filmed in English, but then after the fact it was decided that they should be speaking in their own language instead. So he did something similar, coming up with alien-sounding gibberish that would seem like it matched the actors' mouth movements. And Alley and Nimoy recorded this alien dialog to be dubbed into the scene.
When it came time to work on the next movie, Okrand was brought back to come up with a working Klingon language and coach the actors to actually speak their lines in that language on set.
Kor
