Tionne always had a fascination with Jedi history. So it was a lucky coincidence that she turned out to be one of the many Force-sensitive individuals hanging out in the Galaxy many years after the Great Jedi Purge had supposedly wiped them out. Luke Skywalker trained her at his Praxeum, but she also served as the resident historian. She taught the other trainees (and Luke) about Jedi history thorugh song. A technique that she had picked up on the planet Sesame to get through to people with very short attention spans.
After moving up in rank, Tionne began roaming the Galaxy picking up Jedi-related artifacts. This led to several Indiana Jones-style adventures, fighting against other folks (including previously unheard of Dark Jedi and such) who were interested in the same junk. For some reason she took Anakin Solo and Tahiri Veila with her. It probably wasn't anything improper. Just a little odd and predictably dangerous. Around this time Tionne married Kam Solusar so that she wouldn't have to change her name.