After third form normalization, extra tables shall be created. And the functional determinant are used as primary key in the new table, as foreign key in the modified old table. My question is that following this strategy, the referential integrity enforces that when attributes have to be added to the new table before attributes can be added to the "old" table. one can't add attributes to the "Old" table first. However, in my application, it is more intuitive to add attributes in the old table first. It appears to me the normalization rule is not very applicable in such situation.
Database tables are not just files. In a way, they are also abstract entities. During the process of normalization of an existing dataset, a foreign key must coexist with the table to which it refers, so that referential integrity is never relaxed. In practice, this is not possible, but any intermediate steps should be considered only as implementation level issues.
That said, I can't see why creating the secondary table before updating the "old" table would be counterintuitive.
For the sake of intuitiveness, you can say that the "old" table will disappear, after the normalization process has been finished. Only new tables will be there, including a new version of the old table, with the foreign key already in place, and filled with data.