"Joseph's master." This refers to Potiphar.
She told him this explanation
"She explained it like this"
brought to us
The word "us" refers to Potiphar, his wife, and includes the rest of the household. (See: rc://en/ta/man/translate/figs-inclusive)
came in to mock me
"came in to make a fool of me." Here, the word "mock" is a euphemism for "to seize and to sleep with." AT: "came into where I was and tried to force me to sleep with him" (See: rc://en/ta/man/translate/figs-euphemism)
It came about that
"Then." Potiphar's wife uses this phrase to mark the next event in the account she is telling him about Joseph trying to sleep with her. (See: rc://en/ta/man/translate/writing-newevent)
"ran quickly out of the house"