The fuming occurs because it is an equilibrium, the HCl fumes were once originally H
3O
+ and Cl
-.
Yes, I know the K
a is big because its a strong acid, but the fact it has a K
a means that its an equilibrium. K
a is an equilibrium constant which is just specific for acids.
I don't think theres anything more I can say to help you understand why its an equilibrium!
I'll just wait and see if some proper chemist like mike, Borek, mitch etc. can explain it better to you than I can.
I hope I've helped in one form or another...