For beta, you just need a tube that doesn't absorb all of the beta radiation in the walls of the tube before it can ionize the internal gas. Semiconductor detectors are somewhat good for beta since they don't have to be made with metal walls. This particular tube, the SBM-20, is entirely metal, and as such I expect it would have problems picking up all but the highest energy beta radiation.
As for alpha, you need a specially designed tube. Some I've seen use very thin mica windows to allow alphas into the tube for detection.