When one uses the toilet he flushes it to remove any waste. Once he does istinja of his rear end he is sure the ghusalah of the water has changed colour owning to najasah hence it is najis. When he is purifying himself the ghusalah that has collected at the bottom of the toilet splashes on to his hand.

What is his duty in this instance? If he continues to attempt purification can his hand be restored to purity whilst he is washing his rear end if he is sure water flows from it or does it have to be washed separately?

If he is using kurr water(tank supply), no need to care about the splashed water, as long no najasat parts are there on his hand. (If it is little water (qaleel)) It becomes najis.