I decided to share my experience since it's not very common and I had a really hard time finding anything related to my case on any forums and there are probably users experiencing the same issue. So here it goes.
July 2006. Entered USA on F1 visa at the age of 22.
November 2006. Dad living in the USA received his work sponsored Green Card, applied for mine.
Sometime in 2013 dad got his citizenship, which bumped up my priority date.
December 2013. Priority date became current, started collecting documents for AOS.
End of January 2014. Sent everything over.
February 2014. Received RFE for sponsor's W2 and tax supporting documents for "most recent year". Sent everything from 2013 tax return and related information.
April 2014. Received EAD, a few weeks later the interview was scheduled for May 29. Received the interview notice that pretty much said "bring everything in original, copy and translations".
I spent a month collecting all of the documents we ever sent to them, including stuff they might ask for. I got my dad's naturalization and birth certificates, translated some stuff from Russian. I created an "immigration binder" with a checklist of things I needed and kept adding documents to it up to the last day.
My lawyer advised me to only answer the questions at hand and not volunteer any information. Neither him or my dad could be with me at the interview.
Showed up 20 minutes early, was told to wait 5 more minutes until they could check me in.
After check in waited another 25 minutes, was called in by a IO, a nice older gentleman. He asked to me to stand and raise my right hand and answer his question "do you swear to answer all of the questions truthfully", I said yes. We sat down and he had my case folder right in front of him. He said "your dad became a citizen". I produced the naturalization certificate. He took it, wrote some number down from it, asked whether it was the original, I said yes. He told me to take good care of it. Then he looked up my category in a little book, checked something online and said that my priority date was current. I knew all that, but just nodded. He then looked at the form I-485 and went over the terrorist/crime questions. Saw that all my answers were NO, moved on. Asked if I still lived at the address in the form, I said yes. Then he said that he was going to approve and I should get my card within 2 weeks. I asked if there was something I could take with me as a proof (I felt weird leaving empty handed), but he said no, they don't give anything out anymore, congratulated me, shook my hand and told me that I am now a permanent resided and in 5 years from today I can apply for citizenship.
3 hours later I checked my status online and it says card production. Yay!