Cigarette smoke is all kinds of nasty for anyone's lungs, but especially for asthmatic's lungs. In short, in addition to causing lung damage and being carcinogenic, it's also a bad irritant, which can trigger an asthma attack in individuals sensitive to airborn irritants (I'm one of them). Most of my red zone attacks can be connected to cigarette smoke, actually (which is why I get really irritated when I see people violating the ban on smoking within 10 meters of the entrance to a public building we have in my city - I don't mind if smokers want to destroy their lungs, but I take exception to them destroying mine in the process).

So, definitely, cigarette smoke can trigger an asthma attack.