I guess, to be grammatically consistent they should not have suddenly switched to his from their. There is really no particular reason why one would alternate between different pronouns like that. Your confusion is understandable.
As Nathan Tuggy has already alluded to in this comment, this grammatical phenomenon is know as the singular they. The idea behind it is that since the English language does not have a single third-person singular pronoun that can be used to refer to people regardless of their gender, speakers of English have adopted the use of the pronoun they (his was also used quite a lot in this capacity, especially in the past), which is typically used only for plural things or people, to do that. In formal writing, however, you should probably stick to the phrase his or her and use that instead of their as some consider this usage of the pronoun they ungrammatical. I'm not going to waste my time any longer and just shamelessly quote from the excellent article regarding the use of the singular they in English they've got on Wikipedia:
Singular they is the use in English of the pronoun they or its inflected or derivative forms, them, their, theirs, and themselves (or themself), as an epicene (gender-neutral) singular pronoun. It typically occurs with an antecedent of indeterminate gender, as in sentences such as:
"Somebody left their umbrella in the office. Would they please collect it?"
"The patient should be told at the outset how much they will be required to pay."
"But a journalist should not be forced to reveal their sources."
The singular they had emerged by the 14th century. Though it is commonly employed in everyday English, it has been the target of criticism since the late 19th century. Its use in formal English has increased with the trend toward gender-inclusive language.