Translation:Yesterday he told me that he loves me.
Esperanto has different rules for the sequence of time that are likely to confuse English speakers. There are two correct translations for this sentence: "...that he loves" and "...that he loved." And the only reason there are two translations is that English makes a distinction using that Esperanto makes with adverbs.
"In some languages one must sometimes change the verb form in indirect speech. In Esperanto one always keeps the original verb form." (PMEG 33.8.1)
This is also the same rule as direct speech, so it's actually a lot easier than English - but you do have to forget English tenses!
He said that he loves you. == He said, "I love you."
Li diris: "Mi amas vin." == Li diris ke li amas vin.
If you're the kind of person who likes charts, here is how the Esperanto sequenced tenses translate into English.
diris ke li amis -> said that had loved diris ke li amas -> said that he loved diris ke li amos -> said that he would love
diros ke li amis -> will say that he has loved diros ke li amas -> will say that he loves diros ke li amos -> will say that he will love
This rule applies to all situations where someone or something "knows" "thinks" "wonders" "says" "asks" or anything similar. "She told me where the bathroom was." "Ŝi diris al mi kie la necesejo estas."
Descriptive clauses are different. "I found her near where the bathroom was." "Mi trovas ŝin apud kie la necesejo estis." (PMEG 33.4.2)
ohh, ok, yes I see what you mean now. Yes, you're right, I guess "he said to me that he loves me" does sound ok. I suppose I prefer "he told me that" because, similar to "told" being like a demand or order, it also connotes like a confession (as in him confessing his love for her).