Modern terms for and what we think of as sheet music today didn't come about until the renaissance era which largely started in Italy. Sheet music before that only consisted of various note head shapes, and no lingua franca to speak of since it was the gregorian chants and other church led hymnal songs that we're being written down in Europe during the Middle Ages. Italian Renaissance composers were really the first ones to standardize musical compositions, terms, and instruments.

Did it ever become the default language?

Yes, many Italian terms are found after the Renaissance. To this day musicians (particularly of the "classical" kind) learn a lot of Italian words, but we find instructions in other languages all the time. And this is not new, we can easily find those other languages in the music of the past.

During and after the 19th century we find more and more instructions in languages other than Italian.

The basic terms are Italian probably because 16th century Italian music and theory were very influential (they really had things under control and, as it was already mentioned, many patterns were established back then). Several of the places that now form Italy were wealthy and powerful at times, and the arts really flourished. Artists of all of Europe went there to study and try to make a name for themselves. Even the French willingly sent their most talented artists to study in Italy even after those cities were no longer as powerful and wealthy.

You can survive in many cases just by knowing the Italian versions, but you eventually need to be familiar with terms in other languages (particularly French and German, and more languages if you get into less known authors from more "exotic" places).

People were not apparently too worried about standard things until the (second half of the) 18th century. Really, notation is all over the place, and you find regional practices, names and styles to be quite different. In the 20th century we went back to "whatever floats your boat." We use the terms and symbols standardized after the 18th century, but people add instructions, terms, and anything else they need (including new symbols for all kinds of things) in whatever language (or way) they find useful (and some times in more than one, to make their music accessible to more musicians/listeners).