If someone starts from Juz 10 in Ramadan, does he/ she need to finish the Quran in Juz 10 or does it mean just complete the last Juz in order to get the Ajr of finishing the Quran in Ramadan.
What you need is to complete the recitation of the whole qur'an (from surat al-Fatihah to surat an-Nas) . To perform khatm you don't necessarily need to recite the qur'an in the correct order of the suwar (for example you may recite surat Taha before al-Kahf etc.) . And it is pretty fine to complete the recitation in a different month. So if you started a recitation before Ramadan and reached the 10th Juz' you may go on until you hopefully complete the recitation be it in Ramadan or Shawwal. It is also recommended after a khatm to start a new one.