The nexus between turbulence, particle interaction and interfacial tension is virtually unexplored, despite being highly relevant to a wealth of industrial and environmental settings. Here we investigate it by conducting experiments on non-Brownian spherical particles at the interface of turbulent liquid layers. The latter are electromagnetically stirred in a quasi-two-dimensional apparatus, while the particles are individually tracked. By systematically varying interfacial conditions, turbulence intensity, particle size and concentration from dilute to dense, we map the system behaviour over a wide parameter space. We reveal how the dynamics is governed by the balance of drag, capillarity and lubrication. Based on their scaling, we propose a phase diagram comprising three distinct regimes, characterized by widely different levels of clustering and fluctuating energy of the particles. This is quantitatively confirmed by the experimental results.