It's a direct consequence of two things:
1) The neck is made from very stiff maple...possibly too stiff (it happens).
2) The neck pocket may also be well designed, making for an overall rigid and vibrant structure
3) The maple body may be too dense
I'd put money on it probably being number three given the other aspects can be applied to other Fender Jazz basses which don't have the issues you describe. Using maple isn't always bad but it's very variable and for the cheaper models manufacturers will be less discerning in the wood they use. I have an all maple Spector and a strat with a maple body and both are fine instruments. But they use soft maple, not rock maple. Here are some suggestions:
1) If you don't need to slap, try half wound strings.
2) You could try putting a veneer of softer wood like mahogany under the bridge. This will loosen the acoustic coupling between the strings and instrument, making it less efficient at transferring (dampening) higher and lower frequencies. You'll need to adjust the string height to compensate for the raised bridge so if you like super low action it might not be feasible.
3) You could replace the bridge with something more vintage in design, for example bent steel rather than cast for example. The lower mass will transmit string energy less efficiently.
4) You could also install Bartolini 'darker' flavoured pickups and use a SWR SM400 amp to sweeten things up a bit (this combo is great with bright graphite necks in my experience).