Hi,
At the moment this is how it’s supposed to work – the predictive suggestions only work for the live search results list.
It’s intentional as it’s not possible to tell the user if the query was mispelled on the results page, as it’s controlled by the current theme. I will take this as a feature request though, and will try to add an option to the back-end to show these results either way – even if the user is not notified of the mispelling.