Phenomenon where fumes can relight an extinguished flame
It looks like you accidentally created a combustion mixture.  I checked the Material Safety Data Sheet (MSDS) for several mosquito coils, and in addition to the insecticide, one of them also contained the oxidizer potassium nitrate $\ce{(KNO3)}$.  The burning candle likely had some vaporized paraffin (fuel) in the flame, so when you directed the $\ce{KNO3}$ vapor into the flame, you had heat + fuel + oxidizer = combustion!  You literally set that vapor on fire.  I'd be careful with that: although the MSDS indicated a small amount of $\ce{KNO3}$ in the coil, you could still be injured if you were not prepared.