You should rinse with whatever solvent is appropriate. To transfer organic reaction products it's probably not wise to use water b/c 1) lots or organic compounds are nonpolar and thus may not be very soluble in water 2) water is a pain to remove.
If I'm transferring from one container to another I usually rinse with dichloromethane. Once everything is in the new container and I've rinsed a few times, I remove the dichloromethane so that all that's left in my new container is my product.