Here is an excerpt from the manufacterer:
"Advise patients to rinse the mouth after inhalation of Asmanex TWISTHALER."
So you have both been given good advice.
Long term use of corticosteroids such as asmanex can cause a decrease in the effectiveness of the immune system. While this cannot directly cause cavities, it can affect the protective effect of your saliva, increasing your chance of dental problems.
So to answer your question lizard, its probably a combination of both. I would talk to your dentist about other things you can do to help protect your teeth beyond normal oral hygiene.
ive just been put on the asmanex and my dr said to brush teeth good after use because it can hurt your teeth. have you had any bad side affects from it like racu=ing heart or skiped beats .