By default, the integration supports the Dawn theme and replaces the search form with an Algolia template. Other themes might require a configuration change for the Autocomplete to work. Go to Search Options > Autocomplete > Customize and change the setting for CSS Selector to the selector for the search field in your theme.
If you haven’t customized your Dawn theme, once you’ve enabled InstantSearch and Autocomplete, the CSS selectors should be the following:
If you have customized your theme, you would need to modify the CSS selector and verify if this element exists in your implementation.