could be one of two things that occur to me.

one, if a starter cube isn't engulfed in flame, and getting good oxygen, it will sit there and glow and smolder, sending off puffy white smoke. you need to blow on it to get it flaming again, or just wait for the lump to overtake it and burn it off. also, it can't really affect food taste, unless you put the food on while the wax starter is still not fully consumed, and you'll never do THAT twice.

the other cause can be putting food on before you have a fire going at your desired temp for "a little while". how long? i dunno. i find that it's only ten minutes or so. other wait a half hour... that gives the lump time to ignite fully and hot enough that the smoke coming off it doesn't have as much un-consumed stuff in it.

think of a candle. when you blow it out, that little glowing coal isn't hot enough to efficiently burn the wick, so it smokes like crazy. it's still lit, actually, just a poorly performing fire. a lit candle will more efficiently combust the wick, and so there's much less smoke and more light.