The fumes that you see coming from a glue joint is from the heat that is generated during the anionic polymerization process, the fumes do carry the cyanoacrylate within them, therefore when they come into contact with mucus membranes (such as the nose, throat or eyes) the cyanoacrylate reacts with the moisture contained within these areas and cause a burning sensation. This process is not harmful to the body but can be irritating; in some people it can be extremely irritating. This is not an allergic reaction although some people are sensitized to this.
To prevent problems all you need to do is make sure you move air across the work surface with a small fan. The CA vapors will dissipate very quickly into the air and become saturated within the surrounding air. If you are one of the few people that are very sensitive to the fumes you can use the low odor M100F or M1000F CA, which will not fume and cause problems.
NOTE: Some of the cheap generic/Chinese glues have toxins within them (like Benzene and Chloroform), and the fumes they create can be dangerous. Please use adequate ventilation at all times when using glue.