Well, he did double check her food to see if it was poisoined or not again, so she trusts tht he wont poison her and im assuming that she trusts these ‘supplements’ that the duke is giving her becuz hes jus over protective and doesnt even suspect them to do any harm to her.
I'm sure she assumes that to be made a vampire she'd have to be bit a certain way. Since she's from "our" world. And yes they are in there honeymoon period.
Still since she says she wants to have independence she should push back on his babying a bit more in general.
Just as a reminder....Man she is too trusting. Why would she even need supplements?