A good friend of mine told me that her cat wakes her up most mornings a couple of hours before she is ready to get up (like 5am instead of 7am). This friend is retired so thankfully she can take a nap later if she wants to. But what about those who need to get up for work and just aren't getting the rest they need because their pets, who sleep with them, are on a different time schedule?
My dogs sleep with me and are great, no matter what time I get up in the morning (I work at home so often stay up late, which creates a less structured sleep/wake up time) they will wait until I'm ready to get up before they get up, usually. There have been rare occasions when one of them needed to get up and I was not ready to get up (like at 3am), despite having put them out just a few hours before. But as I said, those times are rare.
For my friend, she doesn't have a door on her bedroom so can't keep the cat out. She just suffers with it. But in a recent article that I read, one suggestion mentioned that for people who work, give the pet something to do during the day when you aren't home. It is not surprising that when you get home from work they want to play since they most likely have been sleeping all day long. If you can walk them in the morning before you leave for work that is also ideal. But make sure you play with them when you get home to get some of that energy that they've stored up all day out of them before going to bed so that they will hopefully sleep through the night and become more adapted to your schedule.