If i were you, i'd stick with the past tense forms.
For more info, I suggest you look up 'reported speech'.
Note: in conversational English, reported speech rules are sometimes bent.
Guy: "I live in Bristol."
Proper: He said (that) he lived in Bristol.
simple present --> simple past
Accepted: He said (that) he lives in Bristol. (It's a statement of fact/of something that is still true.)
Girl: I (have) tried their chocolate cake.
Proper: She said that she had tried their chocolate cake.
simple past/present perfect --> past perfect
Accepted: She said she (has) tried their chocolate cake.