Yes, usually she would say "At the same time as I get ready for bed, my husband gets up". It's a habitual action, so the simple present tense is usually used. However, in this case, she is using the continuous tense for rhetorical purposes. She's trying the place the action in the immediate present to make it more interesting to the interviewer and the readers.
This type of tense change is often used for stories and jokes eg,
Joke: "A man walks into a bar ..." Present tense for a past action.
Story: "So, I go up to this chick, and I say ..." Present tense for a past action. It makes the story seem more alive. It's informal use.
Student or Learner