The red gem-stone button does indeed launch Topas5 but it does not send the inp file that's opened in jEdit
All that the red gem-stone button does is open topas.
The TA button with an arrow is the one that (TAsaveset.bsh macro) is the one that does the sending.
Can you check that you have a file "launch_file.txt" in your topas directory. Rename it to something else, and then press the TAarrow button to run the TAsaveset.bsh macro. The file should reappear and should contain the full path of the file which was active when you pressed the button.
Can you also check that you are in launch mode in Topas. You need to make sure the rocket ship button is active.