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While the tunneling of a particle through classically forbidden barriers can be described by the particle's wave function, this merely gives the probability of tunneling. Although various factors can increase or decrease the probability of tunneling, one can not be certain whether or not tunneling will occur.
When two condensates are placed in a double potential well and the phase and population differences are such that the system is in equilibrium, the population difference will remain fixed. This is not to say that tunneling does not occur — rather, in the event that a particle tunnels through the barrier, another particle tunnels in the opposite direction. Because the identity of individual particles is lost in that case, no tunneling can be observed, and the system is considered to remain at rest.