The mechanism of the onset of magnetic reconnection in collisionless plasmas in the tails of planetary magnetospheres and similar processes in the solar corona is one of the most fundamental and yet not fully solved problems of space plasma physics. Modeling the onset with particle codes requires either extremely large simulation boxes or open boundary conditions. In this Letter we report on simulations of reconnection in the magnetotail that incorporate open boundaries. In a simulation setup with the initial geometry similar to that of the GEM Reconnection Challenge bursts of spontaneous reconnection are detected in outflow regions that mimic magnetotails. They strongly resemble the ion tearing instability predicted by Schindler  as a mechanism of magnetospheric substorms. Quenching the onset by replacing open boundary conditions for particles with their reintroduction reveals the key role of passing particles in the tearing destabilization.