Fantastically, although I havn't driven a Cayman with 19s.
I have R compund tyres, which are hard to get in the right sizes for 19's. I thikn most track junkies are using 18's.
There is now a slight amount of body roll due to the increased grip of the tyres. But its still an amazing handling car. I have had about 6 instructors and professional racing drivers take me around thr track in my car, and they all commented on how well it handled.
These guys drive in Carerra Cup, Touring Cars, open wheelers etc. Whenever I do a drive day I see the instructors come straight to me and ignore the rest as they want to drive my Cayman!