Orandatchi, what you saw is completely normal.
If you allow all of her rice bowls to empty, or her happiness/friendship guage to empty, she'll call for attention. If you haven't tended to her needs within 15 minutes, the attention icon will turn off automatically. However, if several (8 - 12?) hours later, you still haven't tended to her needs, she may become deathly ill.
One time I allowed Makiko to go to bed without tending to her needs. I was woken up at about 4 AM when my Tamagotchi turned its screen on by itself and beeped for attention. I found Makiko face-down on the living room floor with the death angel hovering over her. I was able to summon the ambulance in time to rescue her.