The first mail of any user to each list has to be manually approved.
This manual approval may take hours or even a day depending on which
moderator is online when. Normally the moderator clicks "Allow this
message and all future messages from the same author" and then future
messages by the same author to the same list will appear in a matter
of (normally) seconds. In case of doubt the moderator may also just
approve the current message, and then future messages by the same
author are still subject to approval (this is extremely rare, unless
the moderator clicks the wrong button by mistake); but another
possibility is that a message which the Google interface thinks "looks
spammy", even by a whitelisted author, will have to be specially
approved by a moderator. In most cases the latter are false alarms.
Best regards,
Tony.