I think you are confusing volume snapmirror with qtree snapmirror.
You should be doing a volume snapmirror, if you do this then all snapshots on primary exists on secondary after update, meaning the consistent snapshot you just took. SC does not really support qtree snapmirror, you can do it but SC wont manage secondary snapshots. SC supports snapvault which is qtree snapmirror essentially so if you want different snapshots to be maintained on primary and secondary use snapvault, otherwise use volume snapmirror.
Make sure this option is set NTAP_SNAPMIRROR_USE_SNAPSHOT=N this will ensure SC does a volume snapmirror.