Answer:
Yes, Tammy should ask for an email confirming the telephone conversation if she accepts the job immediately.
Step-by-step explanation:
A job offer is more authentic when there is a reference material to show the provisions such as an employment letter, offer letter or contract of employment.
Apparently, the job in question is not an internship, it will continue even after she graduates which make it even more appropriate to provide formal documentation.
An email will validate the date of the job offer, contain the information of the sender ( HR supervision) and the information of the hiring company. It will also spell out specific details that will guide against misunderstanding and ambiguity.
Another reason why she should ask for an email is to have it handy to present when the need arises even if the HR supervisor that called her to give the job offer is no longer available.