Exactly. However you will not find "glossolalia" in the Greek text of the NT. It is either glossa, glossais, or dialektos. All must be translated today as "languages" (as to several modern bible versions). So the gift of "languages" (spoken supernaturally) was presented in both Acts 2 and 1 Corinthians 12-14. Paul therefore insisted that there be an interpreter, since all languages can be interpreted.
The modern concept of glossolalia is a deviation from this, even though the people who originally promoted tongues in the early 20th century believed that the gift would be actual languages for missionary work. Now one poster said that this actually has happened on the mission field, but I requested documentation to support that, and so far I have not seen any. Missionaries have continued to put time and effort into learning foreign languages and then ministering to those to whom they went.