In quantum cascade laser frequency combs, the intensity distribution of the optical spectrum can be split into two well-separated lobes of longitudinal modes that, even when far apart, have a common phase relation and preserve equal frequency separation. The temporal dynamics of two lasers emitting at 4.4 and 8.1 µm operating in this bilobed regime are here investigated. The laser intensity shows a peculiar temporal behavior associated with the spectral features whereby, every half a round-trip, the total emitted power switches from one lobe to the other, with a perfect temporal anti-correlation. The anti-correlation between the lobes is also observed in the intensity noise figure of the emission. This coherent phenomenon arises from gain nonlinearities induced by spatial hole burning and the extremely fast gain dynamics typical of quantum cascade lasers.