I admit to having just tried to learn about pivot tables. It seems to me that if your pivot table were defined in terms of the named ranges, it should work. But, I attempted this with Google sheets and discovered one cannot tie a pivot table to a named range.
If this is what you have tried (which, I actually think Excel would do automatically), then it's probably not possible. Looking into the documentation for Apache POI, I didn't see anything that suggested a notion of recomputing, only defining again. While it is possible in Apache POI to define a pivot table, the relevant configuration is not offered through Mango and so this would be somewhat of a feat to achieve, currently.