Thanks for the feedback cigroller.
My car is a Mazda3, automatic transmission. It's about 8 yrs old but I hardly drive it so it's only 79,300 km on the odometer.
Well, the situation didn't end there. I spotted an oil spot under my car the next day. Took the car back today and this time, the foreman worked personally on my car (he had his staff doing the repairs the last time). He said it was just residual oil dripping from the oil pan, probably from the engine oil overfill. He cleaned it up and checked for leaks and found none.
I insisted he recheck the transmission oil level, and lo & behold, it was still low (I'm at least grateful he recognized that and admitted it and didn't try to BS me), so he ends up pouring yet another liter in to top up properly.
All told, the Mazda3 is supposed to have ~7.3 L of transmission fluid and they had to top up about 3 L (they claim it was 2 L only but my husband saw them pour in at least two 2 L jugs of oil the first time 'round), so I calculate I was running around with ~40% less oil.
To answer your query cigroller, the car not shifting smoothly into reverse was my first sign something was wrong (would lurched forward before going backward). Later, when I took the car out again, at about 10 km, the car felt like it was dragging, and that's when I saw all the white smoke in my rearview mirror.