Tell me, did he say why he wanted advance notice, or how much notice he wanted? I'm guessing not.
It absolutely is not common to notify your employer when you begin looking for a job.
Job hunts can easily take months (plenty of places have hiring processes that can take that long). Particularly, job-seeking where you already have a stable job, one you'd like to move out of but also aren't desperate to escape immediately, can take any length of time at all. For one thing, you're limited to what you can schedule around your work hours. For another, you're likely to be much pickier about what opportunities you pursue and accept, because you can afford to be patient and selective.
It would be madness to tell your company "Listen, I'm looking to leave" when you have no idea at all how long you're looking at. It means the company stops trusting you and starts working around you; and it means you could be fired and lose your fallback position.
And really, think of all the other ways this just makes no sense at all. Let's say I'm perfectly happy at my job, but then I hear about a really fantastic opportunity somewhere else. I set up an interview. What, I should tell my boss? Of course not -- if I don't get the job, I'm staying right here for the forseeable future. I'm not going to mess that up.
(This, by the way, is a great way to depart smoothly, when the time comes. "I wasn't actively looking, but then I got this really intriguing offer, and I decided to go check it out.")
It is nice to be considerate, to the degree that you can.
There are plenty of legitimate reasons to want longer notice, which you can soothe without shooting yourself in the foot. Being considerate of your current workplace will help you leave a good, friendly, professional impression -- and also, it's the nice thing to do, within reason.
I'd point to two things:
Maximize notice. If you get an offer and your new employer wants you to start in a month, then hey, you can give your boss a month's notice. Better for him. If you get an offer and the start date is flexible, then give yourself time to finish up pressing projects, document stuff, and/or train a replacement (maybe even tell your boss at this point, and ask how much time he wants you for).
This does depend on your new employer's flexibility (you don't want to risk the offer, or a bad impression, so ask "lightly"), and on how much you trust your current boss (not to fire you right away; not to take advantage and keep you on for longer than you want).
Don't wait until you leave to make your issues known. A big problem a lot of companies have is, employees and employers don't really communicate. Employees don't like complaining to their boss (it makes them look bad, or incapable, or unhappy), and also can avoid asking for benefits and raises. The result can be that an employee leaving can really catch them by surprise -- "I never saw it coming!", "I thought everything was OK!", "Why didn't you give me a chance to fix things before it was too late?".
You don't have to leave them flat-footed. It's to their benefit and yours for you to communicate issues to them. Not as "fix this or I'm leaving" (although that's an option, when you need it). But as "Listen, it'd be a real improvement if you fixed this," or, "Listen, I've been here X years, and I'm expecting a raise," or whatever else. Be constructive in criticism, and firm when advancing your own benefits.
This can be a real help against "well why didn't you tell me you were looking for a job." You don't need to tell them whether they've reached a breaking point; that's your call and you keep your own counsel. But it is helpful to tell them what your issues are, what your expectations are; it gives them a chance to at least be in the running to keep you, and feels less like a betrayal if/when you do leave.
All this, of course, is also why it's so important for employers to establish trust and rapport with their employees, and actively encourage openness and criticism. If you discourage employees from bringing you their issues, or give the impression that it won't help, or they'll be branded troublemakers or "not team players," well, don't be surprised if the first you hear about their issues is when they hand in their notice.