Hi Thomas,

You can use the following hook to trigger the indexer yourself.

https://www.admincolumns.com/documentation/action-reference/acp-editing-saved/

Based on the documentation of FacetWP, the hook should look something like this.
Not tested!

/**
 * Updates the post modified data after inline edit
 *
 * @param AC_Column $column Column instance
 * @param int $id Item ID
 * @param string $value User submitted input
 */
function acp_trigger_facet_wp_indexer_after_acp_edit( $column, $id ) {
	if( 'post' === $column->get_list_screen()->get_meta_type() ){
		FWP()->indexer->index( $id );
	}
}
add_action( 'acp/editing/saved', 'acp_trigger_facet_wp_indexer_after_acp_edit', 10, 2 );