Your statement:
We managed to figure out, what is the reason of that issue.
Most likely, the reason is, that the Product you refer to had different Shipping Methods for it, and now they have been changed. Indeed, that is an issue, and it will be fixed in our nearest AliShipping add-on update, there will be added a feature for Update of already added Shipping Methods on your site.
Now you say I'm afraid, but I think that there is no contradiction here. Can't you see the difference?
Why, these warehouses in other countries are not AliExpress? If that is the case, you should remove the "AliExpress" name from the add-on. You should rename the add-on to Shipping Product China Warehouse or anything that indicate it is for China warehouse only. With this name of the add on now, it is deceiving users.