Context. We present a multiwavelength analysis of the simultaneous optical and X-ray light curves of the microquasar V404 Cyg during the June 2015 outburst. Aims. We have performed a comprehensive analysis of all the INTEGRAL/IBIS, JEM–X, and OMC observations during the brightest epoch of the outburst, along with complementary NuSTAR, AAVSO, and VSNET data, to examine the timing relationship between the simultaneous optical and X-ray light curves, in order to understand the emission mechanisms and physical locations. Methods. We have identified all optical flares that have simultaneous X-ray observations, and performed a cross-correlation analysis to estimate the time delays between the optical and soft and hard X-ray emission. We also compared the evolution of the optical and X-ray emission with the hardness ratios. Results. We have identified several types of behaviour during the outburst. On many occasions, the optical flares occur simultaneously with X-ray flares, but at other times, positive and negative time delays between the optical and X-ray emission are measured. Conclusions. We conclude that the observed optical variability is driven by different physical mechanisms, including reprocessing of X-rays in the accretion disc and/or the companion star, interaction of the jet ejections with surrounding material or with previously ejected blobs, and synchrotron emission from the jet.