We report results from simulations in general relativity of magnetized disks accreting onto merging black hole binaries, starting from relaxed disk initial data. The simulations feature an effective, rapid radiative cooling scheme as a limiting case of future treatments with radiative transfer. Here we evolve the systems after binary-disk decoupling through inspiral and merger, and analyze the dependence on the binary mass ratio with q≡mbh/MBH=1,1/2, and 1/4. We find that the luminosity associated with local cooling is larger than the luminosity associated with matter kinetic outflows, while the electromagnetic (Poynting) luminosity associated with bulk transport of magnetic field energy is the smallest. The cooling luminosity around merger is only marginally smaller than that of a single, nonspinning black hole. Incipient jets are launched independently of the mass ratio, while the same initial disk accreting on a single nonspinning black hole does not lead to a jet, as expected. For all mass ratios we see a transient behavior in the collimated, magnetized outflows lasting 2-5 (M/108M⊙) days after merger: the outflows become increasingly magnetically dominated and accelerated to higher velocities, boosting the Poynting luminosity. These sudden changes can alter the electromagnetic emission across the jet and potentially help distinguish mergers of black holes in active galactic nucleus (AGNs) from single accreting black holes based on jet morphology alone.