The tests are 100% reliable in terms of identifying DNA links. The predictors they give for possible relationships are not always (unless it's a parent.) That's where you need to do the paperwork/investigative work to confirm. The ethnicity stuff is here and there - it's become more accurate as more people have tested (generally speaking). But you also need to back that up with your own research to be sure. I will also add another caveat that DNA matches under like 20cm can be a bit of 'noise' but not always. The problem is more that the paper record which might link you to the ancestor is too far back to prove things sometimes. People's reaction to very high unexpected DNA matches is often that it is a 'mistake' - it isn't, honestly, but it does take time to process.
I'm adopted and I did my DNA and discovered my birth father straightaway and confirmed biological ties to my birth mother's family that I knew existed through other means. My birth father was also adopted and I figured out with the help of a genetic genealogist who his parents were.
If enough of your relatives have done DNA a researcher can 'find' you through paper records even if you are not on the sites yourselves. This is why things can be tricky if you want to remain private and you have lots of keen family researchers around you! It can be very invasive.
Some people are ridiculous about their trees being 'accurate' as if they were under notice and making some sort of submission to the courts as part of litigation as opposed to a fun hobby but ultimately a record of people's personal relationships as much as anything else. I have had to beg my new found biological family members with 10K plus people trees not to include some details about the other side of my biological family (who are nothing to do with them whatsoever) out of concern for their privacy. It's been a nightmare TBH.
This tests carry risks and the poster upthread who said she wouldn't be prepared for something to 'come out of the woodwork' is being completely reasonable. I am not offended by that comment. Once you open the door, you can't control what happens next.
I am glad I did it overall but it's not 'just a fun thing' for many people. The sites are getting a bit better about the warnings after all the NPE experiences but it doesn't really sink in until it happens to you.