We present a study of the distribution of X-ray detected active galactic nuclei (AGN) in the five most massive, M₅₀₀^SZ > 10¹⁴ M_⊙, and distant, z ∼ 1, galaxy clusters in the Planck and South Pole Telescope (SPT) surveys. The spatial and thermodynamic individual properties of each cluster have been defined with unprecedented accuracy at this redshift using deep X-ray observations. This is an essential property of our sample in order to precisely determine the R₅₀₀^Y_x radius of the clusters. For our purposes, we computed the X-ray point-like source surface density in 0.5 R₅₀₀^Y_x wide annuli up to a clustercentric distance of 4 R₅₀₀^Y_x, statistically subtracting the background and accounting for the respective average density of optical galaxies. We found a significant excess of X-ray point sources between 2 and 2.5 R₅₀₀^Y_x at the 99.9% confidence level. The results clearly display for the first time strong observational evidence of AGN triggering in the outskirts of high-redshift massive clusters with such a high statistical significance. We argue that the particular conditions at this distance from the cluster centre increase the galaxy merging rate, which is probably the dominant mechanism of AGN triggering in the outskirts of massive clusters.