Since the entire system is thermally insulated, there is no exchange of heat between the system and its surroundings ($q = 0$). By definition, any thermodynamic process where no heat is transferred is an adiabatic process. Additionally, because the gas expands into a vacuum (completely evacuated cylinder B), the external pressure is zero, meaning no work is done ($W = 0$). This is known as free expansion. According to the first law of thermodynamics ($\Delta U = q + W$), the change in internal energy is zero, which also makes it isothermal for an ideal gas. However, the direct restrictive condition provided in the question ('thermally insulated') specifically defines the process as adiabatic.