I've come up with a simple fix that appears to work just fine.

After loading Clank! [Scripted] in Tabletop Simulator click Modding -> Scripting -> Players Table - 960044 and replace the code on the right with this fixed code[pastebin.com] and the Rebels should only draw a card automatically if you have a companion in your play area that isn't themselves. Only tested with base game cards. Don't forget to click save and play afterwards.