Yes, 1.2m is the length as measured from the electron's frame. In your formula above, L_{0} is the proper length of the tube as measured in the frame we are working in, and L is the length as observed by the moving observer. So, suppose we are in the frame at rest relative to the earth. Then, L_{0} is the proper length relative to the earth, L is the length which the electron sees, and v (in the factor gamma) is the relative velocity between the earth and the electron.
