The way it works is this: when the primary MX goes down, the backup MXs queue the mail and keep trying to connect to the primary in order to offload the mail.
The primary may not know that it's unreachable (e.g. it may happen due to network problems), so if waiting for the backup MXs to contact the primary isn't
good enough, you might have to schedule a cron job. I haven't found anything in the documentation suggesting that postfix (in particular, the smtp client part of
it) can be configured to send an ETRN command, so you might have to write a simple script as suggested in this
message from the mailing list.