Weeds - Dandelions - I am concerned

I applied some weed killer the other day, and indeed the dandelions
seem to be in their death throes.  I don't understand though.

I think I read somewhere that the way these weed killers work is they
accelerate weed growth so they demise early.  Accordingly, my
dandelions are wilting now, but it seems to me what has happened is
that they have grown, bloomed and then quickly turned to seed which
the wind is blowing around like it always does.  Well now, doesn't
this mean that I know have new seeds all over my lawn?  Which will
again bloom one day?

Straighten me out here.

Thanks

-GECKO