To change the index that is being queried in the Autocomplete dropdown in Shopify, you'll need to edit the algolia_autocomplete.js.liquid file.
Go to Themes > Current Theme > Actions > Edit Code.
Under Assets we select algolia_autocomplete.js.liquid:
On line 57 we find the "index" function:
An example change is below:
We then press "Save" to execute the change.
We do not recommend making this change without first discussing the impact with the Algolia Support team.