Last week, I had a postdoc interview for a "senior" role. They call it senior because they've asked me to lead on a (perhaps the) research problem. For the interview, they asked me to prepare a 10 minutes presentation where I propose a research plan. My presentation focused on a particular case with a detailed plan. I proposed to work on a particular case simply because it's all I can do at the moment (in terms of my current knowledge and research experience from my Ph.D.).
They complimented my presentation and the fact that I have a clear plan. But they did say that they want someone to work on the research problem from a general perspective and then perhaps at the end, target a particular case. The researcher is also expected to show leadership during his research when working on the project. The issue is the general case will require a lot of reading. The interview was really good and I have answered all of their questions. But they didn't ask much to be honest (I guess it's because my presentation was technical and focused on the particular case and not the whole problem). But I wasn't expecting an offer because our research goals weren't the same.
Now that I gave some background to why I am hesitant, I will get to my question. The PI sent me an informal email just two days after the interview, saying that I did a good interview and I should expect good news. The next day, he did say that he's going to offer me the position (again informally) and that I need to accept so he can send a formal letter. I told him that I am interested but I have another interview next week in which I've confirmed my attendance. I said that we can start the formal procedure next week after my next interview. He basically said that you have 2 days (before my next interview) to accept otherwise he will move to the waiting list. It's my first time receiving an offer, is this normal? To give 2 days as a deadline knowing that I asked for more time for my second interview? Note that a 5 day-deadline is more than enough to have an idea about both postdoc positions!
I want to thank you for answers. Really good points were mentioned that help see things from both sides (candidate's and the PI's point view). For this particular case, I decided to quickly decline the PI's offer informally.