You should be concerned for the following reasons:
"The house is only 40 years old"
they were using asbestos until well into the 70's and later (I don't know the official last date)
As far as 'a mask' if it is any type of paper mask or anything less then a P-100 it won't work. The fibers are so small that even good quality paper dust masks are ineffective.
There are many good resources on the web that can help you do this safely
The tile is not as much of a concern as that backing for vinyl flooring. Most of the fibers stay bound up in tile,