I've got an old Watham I cleaned,

Size 18, model ?1883 I'm told. I removed the sleeve and stem because it was really dirty and rusty. I didn't get a good mark on the location.

Now, it seems like the stem is overly easy to go into setting mode- like the sleeve needs to be moved a few turns. I'm guessing this means it's always partially out- meaning the sleeve should be moved deeper into the case.

Is this correct?

That's correct.