Tar and nicotine are not blue, so forget that idea. What happened was that the size of the smoke particles had changed.
The particles in cigarette smoke as it rises from a quietly burning cigarette are extremely tiny, smaller than the wavelengths of visible light. When a passing light wave encounters one of these tiny particles, the particle is too small to bounce the wave backward like a handball from a wall.
Instead, the wave is merely deflected somewhat from its path and continues off at an angle: It is scattered. The shorter wavelengths of light, at the blue end of the visible light spectrum, are scattered more out of their original paths than the longer wavelengths, because they are closer in size to the smoke particles.
When we look at the smoke with the main source of light behind us or off to one side, many of the blue rays aren’t going straight through and being “lost” to us; they’re being scattered around the room, more so than the other colors. Thus, our eyes receive an excess of bounced-back blue light and the smoke appears bluish.
When a cigarette is puffed upon, the smoke particles are somewhat larger, because they don’t get a chance to burn down completely. When inhaled, many of them get trapped in the lung, where they are not seen again until the biopsy.
Those particles that do complete the round trip to lung land come out coated with moisture, which further increases their size. The particles are now bigger than the wavelengths of all colors of light, and they therefore don’t scatter any of it. Like any large object, they reflect all colors equally, right back to where they came from.
The smoke therefore doesn’t appear to have any particular color and it looks white.