Do I clean (leach) the filter cartridges also?

Filters need better cleaning,maybe backwasing under pressure.

But just washing+leaching will also help.

Carbon, Organic--any type need cleaning and cannot be harmed.

Yes, of course introduction of filter will definitely improve the cleaning process. After cleaning process, if you want to use this filter again immediately there is no need for cleaning. But if you want to use the same filter again after one week or fifteen days, then you must clean and preserve the filter in appropriate container like clean plastic bag or equivalent clean container.

Cleaning of filter can be done first by flushing the filter with sufficient quantity of clean appropriate solvent like water or any thing else as per the material of filter. Then back-washing with the same solvent and again flushing with the same solvent.This will provide proper cleaning to both the sides of filter. FInally after cleaning preserve the filter till next use in clean container as mentioned above.