Any fee would have to be reasonable. If the fee is charged while you are negotiating and they are estimating, this is not reasonable. Once they notify that you need to get it out of there or they will start charging storage you need to do so. They should not be able to retroactively charge storage. Good luck in getting them to change their tactics...
I say NO.
Did they ever tell you that you would be responsible for a storage fee? I assume you were in contact with the shop during the time it was stored there? If it's not in the fine print, you will likely prevail against them in small claims court.
This is my opinion and should not be construed as legal advise for your specific case as there are many more facts which you have not provided.