I agree with the replies so far in that there isn't a major risk of the mushrooms spreading.

That said, it's not completely risk free and I think it's important for folks who decide to get into the hobby at least take a moment to think about it. If you have someone in the household that has respiratory issues, I think it would be worthwhile ensuring that you have good containment to prevent spores from circulating the home (or do it elsewhere). This is particularly true if you decide to scale up (which is natural once you have some success, it truly is fun).

Also the growing environment is subject to infection from whatever environmental molds/fungus/etc are around, so reasonable precautions should be taken when handling/disposing. Once you get your procedures down this is less of an issue but still something to keep in mind.

Personally I didn't do anything but very basic precautions and never had an issue.