I have a question about skill assessment for exam and migration purpose

Can applicants apply for migration after they pass the eligibility/skill assessment or they have to pass the physio exams first? I am confused about the information on the website of the APC. I contacted an immigration agency via a friend but was told that migration application can be started once the skill assessment has been done. But after I read the APC website, it seems not the case.

My concern is it is hard if one cannot move to Oz first before taking the exams. How other people usually do?

Please advise.