Hi,

    1. Usually .ids is used only for returning ids to many2many fields and not for  many2one field.

    2. default works when a record is newly created , when you select create button  to  create a form or when you select add a line , It works on the go. 
    3. Here on the go, there is no data filled in items_id. Only if items_id is available you can check the category of the item.

    3. So i guess default wont work in your case.

                                                            or

 you can have your categry_id  field as a related one like,

categry_id = fields.Many2one('product.category', string='Category', related='items_id.categ_id', store=True)

Related fields wont be stored in database unless you give store = True

                                                    or

Try api.onchange

@api.onchange('items_id')

def onchange_items_id(self):

   if self.items_id:
       self.categry_id = self.items_id.categ_id and self.items_id.categ_id or False
    else:

        self.categry_id = False 

Hope it helps,

Thanks