this is just part of her growing up. typically around 3 months old, babies will all of a sudden "wake up"! this is a good thing. it means shes growing, and healthy, and ready to experience more of the world! it feels so wierd because shes been sleeping so much so far, but now its just time for her to wake up and start learning more about the world! :) tummy time is going to start being more fun and more easy for her to do in small amounts of time.... reading books, playing with toys (or eating them) ... or just watching things around the house! get a sling and just have her in that with you during the day, facing out, and she can see what you are doing and you can talk to her about what you are doing. this teaches her a lot, and increases her vocabulary by leaps and bounds, even if she doesnt start talking for a while yet! :)
its normal and perfectly on time for her to wake up. try to follow her schedule. it sounds like what you were doing was working, but it wont anymore. its very common for it to stop working at some point because babies will change their sleep needs. i wouldnt even be surprised when in a month or so you start wondering what happened to her sleep at night! (developmental growth also causes sleep disterbances; so rolling over, crawling, etc will mess with her sleep)
this is the time where you need to just watch her signals. babies will get tired and they will give you plenty of signs that they are tired. running it by the clock isnt a reliable way to do things, and it undermines your instincts and ability to trust yourself to understand the communication that your baby has for you. rubbing the eyes is a sign of being tired. also fussiness is also a sign of crying, especially if you have tried everything else. babies typically arent ready to fall asleep on their own, and even though she has been, she might not now. always be sensitive to her needs. if you have that sling, that is also a fantastic place for her to snuggle in and get ready for sleep.
the moby wrap is my favorite sling. :)
anyway, just trust yourself. that book doesnt know your child, neither does the author. though methods and ideas are good, none of that matters if your heart, and your instincts tell you something different. :)