I've learned this the hard way, through experience:

When you eat a meal, tiny little food particles can remain stuck to the
back of your throat for a while after eating.  Especially if they're
fibrous and don't dissolve well, like vegetables.

Then when I irrigate, some of that saline solution gets down the back of
my throat and actually washes a few of those food particles into my
windpipe.  This feels very irritating (just as if I'm congested with
phlegm), until my cilia can work on them and I can cough them out.

So I've learned the hard way always to rinse my mouth thoroughly with
mouthwash *before* irrigating, to make sure nothing funky in my mouth
can get swept down my throat into my windpipe by irrigating.