I recall somebody saying something along the lines of "She's [Cordelia] in there, just very deep down" - or something like that anyway.
Presumably this is her soul, the thing that makes her Cordelia. The issues are too confused in the verse to try and untangle, but lets work with that. Taking a suitably Cartesian approach to matters, there has to be some psycho-physical interaction going on then, between the brain and the mind (soul, self, whatever).
So perhaps it was that Jasmine was in control - in place of where Cordelia's soul would normally be. Jasmine's essence or soul had to communicate with Cordy's brain, so whatever Jasmine wanted was being put through a 'Cordy' filter which is why she still sounded and acted so much like her... if that makes much sense!
And, let's remember, it is a TV show and the writers have to create conflict and intrigue and this was a very good way to keep us hanging on.