Thank you for contacting us with this and for your update.
I'm glad that now you can run all the necessary tests directly in The Welkin Suite IDE.
The reason for this behavior is the next:
when you open the 'Run tests' wizard, you can see the list of tests from a cache - the caching of this information helps to avoid loading the list each time since this can take a lot of time;
you can see the date/time of saving the list to the cache when navigating to an 'Info' icon.
After refreshing the list you get all the updated information from your Salesforce org even if some of the tests are absent in your TWS project.
If you would have any other questions, please let me know. I will be happy to answer them.