I see that you have got accepted into IIM Jammu but still are willing to switch to a better IIM.

Regarding the fees, lessening you will have to refer to the prospectus. I think there is a certain date beyond which there might be a fixed deduction. 

But this process of deduction and refund will take place at IIM Jammu itself and does not concern the new IIM you will be joining.

So whichever institute you are joining next, the admission process and fees deposition will begin afresh.