You need to remove that trap. Not only is it an S-trap, it will affect the overall flushing ability of the toilet, especially a modern one with low-flow, and siphon things, as you've found. It will allow the toilet to fill with water on the outlet side of the weir for a bit, and siphon water out of the toilet. The jet that starts the siphon in the new toilet may not have enough velocity and duration to give a very high evacuation capability of the toilet, but once it starts, if it starts, it should work as the volume in the lower trap will help pull things out. Modern toilets mostly function very quickly...does yours seem more like an older one that relies on the bowl filling up before it starts to flush? That would be my guess.