When you blew your last turbo it blew oil into the Exhaust, a few days of Heavy driving or a few days of Normal driving should burn it all out... IF the smoke is blue.
If its not that then your Oil Seal in your Turbo is gone, if the Smoke is white.. Get another turbo, New or Rebuilt ones should come with a Warranty though.
Not sure if you’ll see this but I had my A4 b8 turbo replaced with a used turbo from a 2015 A4 with 51k miles on it. I haven’t even driven it for 50mi to have all the oil in it (from the install job) that’s not supposed to be where it’s at, burnt off, yet I’m concerned about the blueish smoke coming out between the turbo and side of engine, around the exhaust manifold. Get this tho, I also had injectors replaced and they’re currently replacing HPFP cuz I had gas in my oil, oil that was there when I initially took it to the mechanic for turbo & injector job. As I said, I haven’t even got 50mi with it & today as I was taking it back, the minimum oil level add 1 quart max you may keep driving light came on for the first time ever, pulled the dipstick out wiped it put it back and out again and THERE WAS NOTHING on the stick NOTHING (ok maybe about 1/4 of the minimum harsh marks but that’s basically nothing) I don’t know how I drove it before the light came on, but couple of days before I had the turbo replaced the oil was on max; but probably with a little or a ton of gas idk.
They said they’ll make sure everything is fine and of course I was gonna change my oil after replacing the HPFP. I just hope the blue smoke is oil in the turbo burning off but where did all my oil go, guess I’ll find out. Plus I don’t have blue smoke from the exhaust just normal vapor looking like kind of smoke that isn’t there all the time, this is how it was before the turbo installation, and I didn’t blow the old turbo.