CITES has three lists, which are there to control trade through legitimate channels. The way I understand it, the rosewoods (Dalbergia) family has been placed on appendix 2, which means "not necessarily now threatened with extinction but that may become so unless trade is closely controlled" so movement of these timbers across country borders can only legally take place with CITES certification. What this will undoubtedly mean is that those species of wood being controlled will get more expensive.
Where I think this gets interesting is that re-export is also controlled so a permit would need to be applied (and paid) for to export anything containing wood listed on appendix 2, so if you made a hollow form with a blackwood finial or a cocobolo pen, it would be costly to export. This still applies to wood purchased before the 2nd of January 2017!
This article might be of interest
https://reverb.com/uk/news/new-cites-regulations-for-all-rosewood-speciesHere's a link to the CITES appendices
https://cites.org/eng/app/index.phpI sometimes wonder if perhaps more thought should be given to the sustainability of some of the woods being sold for woodturning. A more responsible approach from importers, dealers and ultimately users could remove the need for intervention by organisations like CITES.