I've seen this type of behaviour in many companies I worked for. As soon as you pick up a task that is not related to your job description and do it well, it becomes your responsibility. Usually this ends up as unpaid work that just clutters your daily log. In extreme cases it forces expensive context switches that totally disrupt your daily activities. In my line of work, I often have to pick up the parts that developers or sysadmins are unwilling or unable to complete and do them myself or mock them so I can test a system as a whole or a very specific component in isolation.
Now I'm hard working and results oriented, so I don't mind a bit of extra work if it gets nice results at the end and it helps me grow professionally. This is not your case however. Your manager did not assign you extra tasks to help you grow as a professional or to improve a failing process. She probably did it because heshe didn't want to hire a professional. Regardless of her reasons, it's your job to just say no.
Another thing I learned in my career is to say no. Say no to extra work with no pay. Say no to extra responsibilities without reward. Say no to management roles without authority. Say no to tasks you don't understand or are unsure you can perform. Say no to needy colleagues that can't finish their own tasks on time and constantly need your (untracked) support. Just say no. No one will think less of you for it. And if they do, they aren't being professional and you shouldn't be working for them.