I got the medical request on March 2nd, 2020. One day later, March 3rd, 2020, I received Pre-arrival letter. I took the exam March 5th, and passed on March 8.
I cannt tell medical request coming from Singapore or Sydney since there is no email or information attached in the request letter.
From the gcms notes, Singapore reviewed my case, sending information back and forth to Sydney in mid of January. Sydney passed the eligibility during that time and reply back to Singapore: medical ready to assessed. Then Singapore send the medical request, little late, should be end of January, but somehow they send the request early March. I believed they send the request in batch.
Singapore might changed their process, by sending pre-arrival letter earlier then medical in the second last stage. Background ( criminality can be done at the begining, right after bio/fingerprint received. ) Info sharing can be done before medical and security is the last step, as in my case.