I recently ran into this issue when using react-select components in a modal. For mobile the contents of the modal are scrollable. In this particular case, the Select was at the bottom of the content. Activating the Select made the container overflow and scrollable.
Maybe the container notion of http://react-bootstrap.github.io/react-overlays/examples/ might make sense?
Alternatively, maybe make use of https://github.com/souporserious/react-tether?