I'm not sure what the proper process should be for the scenario you've outlined - one of the mods may be able to provide a definitive answer.
Each time I attempt to use the migration option, I end up asking myself the same question as you've asked, and wondering what the proper process should be... Without then asking on Meta :-)
What I normally end up doing is flag as off-topic, then use the "Other (add a comment explaining what is wrong)" option, and then manually suggest the other site that it should be migrated to. Again, this may or may not be the most desirable way of doing things.
EDIT: as per a linked answer in @greenonline's post , apparently this feature is only available for moderators.
Migrating to an arbitrary stack exchange site This is only an option
for ♦ moderators, so instead of voting to close the question † you
should flag it for moderator attention ‡ with a suggestion of where it
should be migrated.
On established sites, migration paths are created to allow migration
without moderator approval, but any migrations outside of those
pathways still have to be handled by a moderator
The above provided solution of manually suggesting the site by using other option or flagging for moderator intervention are the options.