My Gen.1 does this and I don't have PSE. It's more noticeable because I have a Carnewal exhaust.
This is from the tech manual, posted elsewhere:
Starting phase of DFI engines with high-pressure stratified charge injection High-pressure stratified charge injection is used in the DFI flat-six engines in order to optimise cold starting with regard to fuel consumption and emissions. In this process, fuel is injected once into the specially shaped piston recess just prior to the end of the compression stroke when the engine is being started. This forms a stratified charge around the spark plug to ensure that an ignitable mixture is formed. This reduces both the amount of fuel required and the emissions during the starting phase compared to intake manifold injection. Catalytic-converter heating phase of DFI engines with dual injection Once the high-pressure stratified charge injection starts the engine, the engine management system switches to the catalytic converter heating phase. In this operating state, multiple injection helps to bring the catalytic converter to the temperature required for optimal conversion of pollutants as quickly as possible. To this end, the first injection of fuel takes place during the intake stroke and the second injection of fuel occurs into the piston recess when the intake valves are closed, just before the end of the compression stroke. The slightly lean air/fuel mixture (lambda value approx. 1.05) can then be ignited at a very late point, thus increasing the exhaust temperature. The resulting delayed combustion and the continued exothermic oxidation of unburnt fuel (excess oxygen) even after the exhaust valves are opened produce a considerably higher exhaust temperature directly with the use of dual injection to heat the catalytic converters. The high exhaust temperature quickly heats the catalytic converters to the temperature for optimal conversion of pollutants. As a result, emissions during the warm-up phase are significantly reduced and the secondary air pumps are no longer required for all engines.