Yes, post tags are supported in premium version of WP Twitter Auto Publish with support for custom hash tag and post tags as hash tags .
In WP Twitter Auto Publish , you need to manually add the post tags at message format section in the metabox for each post.
{POST_TITLE},{PERMALINK},{POST_EXCERPT},{POST_CONTENT},{BLOG_TITLE} ,{USER_NICENAME},{POST_ID},{POST_TAGS},{POST_CATEGORY} ,{SHORTLINK} ,{POST_PUBLISH_DATE}, {USER_DISPLAY_NAME} and
{POSTMETA:META_KEY_NAME} – Insert the post meta value corresponding to meta key name. are the supported message format in the premium version.
Also You can limit the content of {POST_TITLE}, {POST_EXCERPT}, {POST_TAGS} and {POST_CONTENT} using below format.
{POST_CONTENT:L-2} to use 2 lines from content
{POST_CONTENT:W-3} to use 3 words from content
{POST_TAGS:3} to use first 3 tags from post tags
For more details please visit ,
https://xyzscripts.com/wordpress-plugins/social-media-auto-publish/details
https://help.xyzscripts.com/docs/social-media-auto-publish/
Hope this helps.