Unless more unpacking is requested, the movers will generally only include unpacking your mattresses at destination. Be advised that unpacking of boxes only entails removing items from the box and placing them on a flat surface. If you would like the movers to put away your packed belongings this is an additional expense that should be requested of the mover at the time of your estimate.
If you find any damage during the unpacking, keep a notepad listing the damaged item and the inventory number for the particular carton. If it is a box you packed yourself, save the box. It may be helpful in settling your claim.