Yes the anenome packs a powerful sting, Killing and hurting corals along the way. Most anenome will travel because it is unhappy, or there has been a change in it's surroundings. Usually if tank remains stable with very little change they will settle in a happy spot remain for long periods.
My first anenome was a condy. It remain in the same place for a year before I got rid of it.[ Got way to big to quick in my 55 gal
] I have a BTA as well she has remained in the same rock for over two years now and has split twice. HTH