I was going to have the second interview today at 16:00. I went there 15:35.
This is your first mistake. It is fine to get to an interview early, but wait somewhere other than in the bosses office.
It's inconvenient for an interviewer to have to change their plans. Get there early, but wait until 5-10 minutes before the interview before talking to the company.
A practical reason is perhaps what you just experienced. If you arrive only a bit before your interview the interviewer will get a ping/call/IM from the front desk saying, "Candidate is here" and then you can leave nearly immediately to go meet the candidate and begin the interview.
If you show up 25 min early, this ping happens way too early for Manager B and it's entirely possible to forget about the interview or get caught into a conversation and forgot you were going to interview. You are then relying on another ping to the manager in order for them to definitely remember.
I waited until 16:30 and then said them I was leaving, since I had to be elsewhere by 17:20.
A few things here. First, always plan on an interview going long-ish unless you have a defined end time from the company. If your interview had gone until 17:00 from 16:00 when it was supposed to be, would this have worked out for you?
Second, don't just get there 25 minutes early, wait, and then leave another hour later.
The way this should work:
- Arrive 5-10 minutes early
- Talk to someone
- 10 minutes after interview was supposed to start, at latest, ask someone for an update and get a time you should hear from them
- Followup again at that time
- If it's 30 minutes later and you need to leave, tell them that you have an appointment that requires you to leave by X
- Also figure out next steps at this point. It's possible something blew up and Manager B just couldn't get away. Who knows. But figure out what the next steps are at this point in the process, to avoid super awkward followup questions
If this is such an important thing for you (early interview ending) make sure to figure this out ahead of time with the company in your correspondence.
Would it be rude to inform Company A manager about this? I fear the interviewer will say Company A that I didn't go to the interview in revenge for not waiting.
It's nearly never a good idea to badmouth a previous employer in an interview and most certainly not a good idea to do so to your potential future employer.
What you could do is touch base with Manager A a few days after you hear back from Manager B (or HR, or whatever) and ask. Hopefully you got contact information or had "next steps" from them when you walked out.