The order of the tags is based on the order of the articles. In the module settings, you can change the order of the articles. The default is "Publish Date Descending," to display the most recent first. The module then retrieves the list of articles to display, then retrieves the tags from the list. You can try using one of the article order filters to see if it suits your needs.
If you need to display the most recent articles first and always use the same tags, you can try using flexbox in the filter container and then assign an order using order. If you find this helpful, customize the following CSS to your needs and paste it into your template's custom.css.
Code:
.ut-articles-pro .filter-options {display:flex;flex-wrap: wrap;}
.ut-articles-pro .filter-options a[data-group="*"] {order:1;}
.ut-articles-pro .filter-options a[data-group=".Joomla"] {order:2;}
And you can continue according to your needs. Use the Element Inspector to identify which group each filter element belongs to.
