First, she was correct to start the hormone pills on the first day of her period.
When you say her period is a week early, do you mean she starts it when she's on the third week of hormone pills? Normally, your period starts during the week you're on the inactive (placebo) pills. If she starts bleeding before that, it's possible she's experiencing breakthrough bleeding. That's sometimes a side effect of the pill, but it usually stops after the first few months.
As for her face breaking out, I have heard of that happening for some people. If this continues to be a problem for her, she can try a different pill. Your body can react in completely different ways depending on which pill you're taking, so one type could make her break out while another type could help clear her skin. Sometimes you have to try several different types before you find the one you like best :)