New development site redirects to live site.

Well, your Dev Site link has already been indexed by Googie, by publishing it here.
But you could make it a little easier on you, by removing that Subdomain Crab,
and just address everything, by example like: https:// yourshop .com/dev/

You could always later add a DOT in Front of the SubDirectory, (site/.dev/...)
and re-link it in the different files, to make it more 'private' this way.
Good Luck!
Ernie