All bonus for AeroplanPlus card post on next statement. Recently did a Self-Referral from my AeroPlat to AeroGold (AMEX) and got the 15K referral bonus on next AeroPlat statement date. And I didn't have any transaction, so like others had been stating where I do not have a statement generated, but I got the miles on Aeroplan account at the right time.
In regarding your referral bonus, it really depend which card you select at Step 1 of the referral screen.
My wife selected the aeroplus gold at step 1 even though she has the aeroplus basic.

That's why I am very anxious to know which referral bonus she will receive.