White puff of smoke was likely water flashing to steam as it hit your exhaust components. Oil may have been there for a while and you just noticed it because you were looking for signs of some type of damage. Had your motor ingested enough water to cause damage (hydro lock) the car would have immediately stopped running. Oil spray under the hood is a common problem with these cars from a poorly designed oil filler cap/user error.
2011 Le Mans Blue M3// Black extended Novillo w/ Blue Grey Aluminum trim/DCT/ZTP/ZCW/ZPP/ZCP Premium Sound ///Akrapovic Evolution Exhaust
2012 Le Mans Blue 135i M Pkg DCT
2008 Brilliant Red Audi TT 3.2 Quattro 6M