Yes, in Sibelius text is attached to a rhythmic position and may be placed relative to the staff, the system, or the page margins. As such, for example, a header or footnote appearing at the margin may move to another page along with the bar it’s attached to. This behavior drew criticism from users who wanted text attached to a certain page, as in Finale – i.e. regardless of how the music flows around it. I find it hard to imagine the latter use case in a music score.
For the OP, I would just attach staff text to the last bar, flip it below, position it in engrave mode, and shorten the frame on the last page if necessary so the text fits nicely.