Come on guys, if the smoke's white, then it's fuel, if it's blue then it's oil and if it's black then it is no good at all!!
Most of these engines have air pressure (that is engine air P off x stage bleed) used to seal the oil bearings. When shuting down the engine, the decay of the sealing air is quicker than the oil P, still pumping some oil "overboard". Next time you start, there comes the blue smoke...
------------------
... cut my wings and I'll die ...