Correct, but the point is if Alice doesn't get a tail, that means she got a head, so she is still in the same position as she was before the flip, only needing

Correct, but the point is if Alice doesn't get a tail, that means she got a head, so she is still in the same position as she was before the flip, only needing a single tail to complete the sequence. If Bob gets a head, then a tail, he now needs two consecutive heads to complete his sequence.