Normally while the Stoven is running you keep the Weber kettle vents closed. The tube smoker sits right on the bottom grate or the heat diffuser and works fine with the vents closed while the Stoven is running.
However, when cold smoking (with the Stoven not running), I have to open the Kettle's top & bottom vents or the tube struggles and goes out.
With the Stoven you do have the option of turning the unit on and running the fan only, but in my opinion opening the vents for cold smoking works better.