If you look carefully, you'll notice smoke is mostly ocurring when the afterburner is turning on or off*. There is a circa two-second process when the afterburner turns on or off during which the fuel injection nozzles are working but the flame is not lit, meaning the aircraft leaves a visible cloud of uncombusted fuel. This is quite normal for engines of all kinds but it does seem especially noticable with the Typhoon. The Typhoon does not use a Rolls Royce engine, it uses an EJ200 which - although based on a Rolls Royce product - has been redesigned and is produced by Eurojet Turbo. *Note you can't always see the exhaust buckets during these transitions because a lot of the power changes occur while the aircraft is pointing its nose at the crowd. This is intentional; afterburner off while flying towards the crowd to avoid busting the display line, then just before turning away from the spectators, engage the reheat so that the flame is visible before the aircraft passes the crowd. This is why the clouds of smoke often occur as the nose of the aircraft is pointing towards the crowd, just before it flies past the spectators.