"References" can be a somewhat overloaded term. If they are simply looking for employment verification then you don't need to give anyone a heads up, and they'll be likely talking to a HR person that may not know you anyway. It's not clear if this is the case but kinda sounds like it, if they just want "employer contact information" from all your employers.
If they actually want references in the sense of people to talk to about you, then yes you should warn (really, "ask") people you intend to use as references. You also want to choose these people, keeping in mind that people - especially managers - still employed by that company may be constrained from talking about you by HR rules. The best references are those who are prepared and willing to speak positively of you. They don't have to be managers, they could be coworkers... Sometimes the request will specify the kind of references they want (e.g. manager, peer, personal) but if they don't, you get to choose people you think will come across the best.
If you're not sure which you need to provide - ask.