There is no single answer to this - both my children lived with me post 18 for a bit and returned home after university for a bit. I guess in this situation it was more a natural continuation of the rules that had applied as they were growing up.
Rules when they were 4 were very different to the rules when they were 16.
The rules did not change on the day they turned 18 - but I guess in essence I continued to run the home as I had done before and whilst I asked far less questions about where they were going or how they spent their time - I was still annoyed if they left dirty clothes around etc.
However, 5 years ago my daughter and son-in-law moved back in with me - she was then aged 29 with 2 children. We did it to enable us to share the finances which allowed her to be a SAHM and HE her children and me to semi-retire.
5 years on it still works great - but there is no way in this world or the next it would work if I imposed the my house/my rules line.
She is still my adult child living in my house as she was at 19 but there is no way I would expect my word to be law. I do pay all the bills so this still applies but it would be ridiculous to not allow them a say on anything.
We negotiate everything and of course we moan at each other about small niggles - but it is definitely a two way process.
I think the original question is relating to the 19/20 year olds rather than our situation but everyone's situation is so different I think it is difficult to have an absolute yes or no on this.
I think if you treat other people with respect and dignity it is unlikely you will have too many issues going forward in any way.