♦ Stacy's financial information is securely stored online.

(Stacy's financial information)?

♦ Aaron's bank statement should be stored securely online with Stacys.
(Aaron's bank statement)?

♦ Seth's students are learning how to effectively store personal financial information.
(Seth's students)?

Are these sentences correctly using possessives?

Right -- except you missed a possessive in this sentence:

Aaron's bank statement should be stored securely online with Stacys.
(Aaron's bank statement)?

Yes, these sentences are correctly using possessives. Possessives are used to show ownership or possession. In each sentence, the possessive form is used correctly to indicate that the financial information belongs to Stacy, Aaron, and Seth's students respectively.