You can upgrade your extension to the latest version (or at least 3.16.1) to easily enable and implement Algolia's Dynamic Facet display features as described here: https://www.algolia.com/doc/integration/magento-2/merchandising/merchandising-studio#dynamic-facets
Alternatively, you can edit the configuration for the widget via the code. Here is documentation on the widgets used in Magento. You can view the widget for refinementList and the sortBy options for this or write a a mixin on the getRefinementListOptions method. To sort facet values alphabetically you should set the sortBy value to “name:asc”. As described in our documentation, to add or change the preconfigured widget, you can use the beforeWidgetInitialization or the new beforeFacetInitialization hook as described here