You are not using interlocking pavers (tight joints) if you have 15" x 15" units and they are probably just stepping stones about 1 5/8" thick. Normally, real pavers are smaller and laid with very tight joints on a uniform 1" thick (no more!) layer of concrete sand. Because of the greater thickness and smaller size, they are more stable. These are laid using a layer of fine sand (masonry sand) spread over the surface and vibrated with a plate vibrator to true up the surface and force or draw the fine sand and the setting bed sand into the joints for maximum strength since units are over 8000 psi and can carry much heavier loads than the larger, thin stepping stones.
If you will not be putting any appreciable load on the patio, you should try to get some compaction on the surface and then rely on the polymeric sand as a "crutch" to hold the surface true. If the 15x15 pavers are typical for that size, strength and thickness, you may not be able use a vibratory compactor without seeing some cracking.