Hmm, so if I understand you correctly, you are asking why you use that as a subordinating conjunction in one sentence and not the other. "He said THAT he travelled a lot in his job. She told me (THAT) they had lived in China for 5 years." The answer is... there is no difference. Using the word 'that' in this sense is entirely optional. You SHOULD use the word that in a strict grammatical sense, but native speakers will do both without noticing a difference. Both sound completely normal to me. This phenomenon is called an empty complementizer. So therefore you could also say: He said he travelled a lot in his job. She told me that they had lived in China for 5 years. I hope (that) this helps! ;)

Use "that" with restrictive clauses. A restrictive clause is one that limits -- or restricts --the identity of the subject in some way. When writing a restrictive clause, introduce it with the word "that" and no comma. (However, if the subject is or was a human being, use "who" to introduce the clause.) Example of correct Restrictive Use: The painting that was hanging in the foyer was stolen. Explanation: The use of "that" in this sentence is correct if the reader intends to single out the one painting that was in the foyer as the stolen painting. However, if there were several paintings hanging in the foyer, this use would be incorrect, since it would mislead the reader into believing that there had been only one painting in the foyer. The restriction here tells us that the one painting that had been hanging in the foyer was stolen -- not the painting in the living room, or the one in the drawing room, or any of those in the parlor.