Magnetic domain evolution at the spin reorientation transition (SRT) of (Fe/Ni)/Cu/Ni/Cu(001) is investigated using photoemission electron microscopy. While the (Fe/Ni) layer exhibits the SRT, the interlayer coupling of the perpendicularly magnetized Ni layer to the (Fe/Ni) layer serves as a virtual perpendicular magnetic field exerted on the (Fe/Ni) layer. We find that the perpendicular virtual magnetic field breaks the up-down symmetry of the (Fe/Ni) stripe domains to induce a net magnetization in the normal direction of the film. Moreover, as the virtual magnetic field increases to exceed a critical field, the stripe domain phase evolves into a bubble domain phase. Although the critical field depends on the Fe film thickness, we show that the area fraction of the minority domain exhibits a universal value that determines the stripe-to-bubble phase transition.