Normally, superglue in the tube is made up of lots of little units (monomers), which, when the glue cures, link up to become long chains of those units (polymers).
In order to start the reaction off some water is normally needed.. damp things stick better/quicker than dry ones and the glue goes hard faster on a humid day.
Only about 40% of the volume of a piece of balsa is solid substance. To give a balsa tree the strength it needs to stand in the jungle, nature pumps each balsa cell full of water until they become rigid - like a car tire full of air. Green balsa wood typically contains five times as much water by weight as it has actual wood substance, compared to most hardwoods which contain very little water in relation to wood substance - it is then klin dried.
Since the reaction gives out heat, the balsa therefore gets hot (and as it becomes hotter so the reaction goes faster - there would be a reaction occuring faster than normal visable via smoke )
I wouldn't like to guess what the fumes might be, as I don't know which out of the cyanoacrylate or the balsa would break down first, and to what extent any nasties would be burnt before evaporating. The gas might be C02 and some other carbon/hydrogen molecules, maybe H2O as well.