Are you sure that the superglue "reacts" with the sodium bicarbonate. Are you sure that is would not do the same with chalk (calcium carbonate). If superglue sets around some powder, it usually results in very strong cement. Do try with chalk powder, or with sawdust. Please be very careful with superglue.

The question seems to be whether the superglue just sticks the baking soda together really well or whether there is some additional chemistry involved. I haven't read enough to have an opinion about it. I left a drop of superglue on my desktop, and it dried into a super-hard spot; I don't know if the baking soda makes it harder and stronger or not.

The bicarbonate (even water) starts the reaction between one cyanoacrylate and another one. The bicarbonate and cyanoacrylate form an ion which reacts with another cyanoacrylate molecule. This starts a chain reaction (polymerization) which ends up a very good adhesive.

A monomer, such as methylcyanoacrylate (the substance in super glue), with two electron -withdrawing substituents can be polymerized with very mild nucleophiles such as Br, CN, amines or OH. The monomer polymerizes on contact with many surfaces. Most often it is initialized by the presence of water (the OH ions from water). If you have sodium bicarbonte present, traces of water (from the surface or air) will react and make NaOH. The reaction is the following:

NaHCO₃ + H₂O -----> NaOH + H₂CO₃NaOH

is a very good starter of the polymerization reaction. It will make the reaction go very fast. Since this is an exothermic reaction (energy gets released) the H₂CO₃ will break up into H₂O and CO₂ . The water will evaporate and that should be the fume you have noticed. You should also see the CO₂. This is my guess on what is happening.