How did you transfer them?

Drag/Drop? (if so, just dragging tracks, or using the Drag/Drop feature in RB .. or DAW)
I've transferred files many ways. At most convenient level I've selected a track in RB and simply dragged it into Reaper (by grabbing the Track number in RB and dragging it to the Reaper Track area) while both were open.

On other projects I've had to export each track, which can have differing results, a couple of possibilities were mentioned above as for the reason (Tempo difference, Acidized track, etc.).
Knowing how you transferred them could narrow down possible fixes fairly quickly.

There's also "Save Track to file" in some versions .. lot's of different ways to do this.

Make your sound your own!
.. I do not work here, but the benefits are still awesome