Are allergic tests for cats definitive? Will the test be done for all for major allergens known in cats?

Depends. There are two materials used for cat allergy testing - hair & skin. Both contain the major cat allergen. Cat skin contains other allergens - especially cat Albumin - not present in cat hair - that sometimes cause allergic symptoms. So if you were tested only with cat hair perhaps you could be retested with cat skin (aka cat epidermal or cat dander).
Cat allergy test. Like any test, cat allergy test results have to correlate with the patient's history. They can be falsely positive and negative.
CAT ALLERGIES. There are skin tests and blood tests for possible cat allergies. Your general doctor or allergist will be able to explain these to you. These tests are not 100% correct.