It happens not infrequently.

Of course, maybe the same people are just susceptible to both.

But I have had sinusitis for decades and not feel that I am likely to get
asthma....

It did in my case.  I had chronic sinusitis for about 15 years before
developing asthma.

Yes, I has a chronic fungal sinusitis, operated....and had frequent
complains of bronchitis, often referred to by some doctors as an asthma
case....what happens is that the infected mucous falls into the lungs
as post nasal drip...and causes secondary infection in the lungs........