How did the acid burnt Man in Alien Covenant die?

This is a different subject than my last dock structure question I asked earlier. However this is a smaller spoiler.

In Alien Covenant, when David watched over the man, whose character/Actor name escape me at the moment, that got his face burned. I believe there were at least "two distinct" different opportunities for him to be impregnated with Xenomorph. I am trying to figure out which one was the most likely. He got his face burn off after a briefly being "face hugged" by a facehugger and someone manage to cut it off. Thus resulting in the acid burn. Was the brief contact enough?

I thought about an alternative scenario which would have the same consequence both literally and figuratively.

Keep in mind that David and not Walter manage to get on-board the fleeing cargo lifter while the audience don't know about David replacing Walter. At the very end David reveal that he managed to save at least two facehugger encapsulated in something inside his own body. Would it have been far more likely that he took out one of those and impregnated him when he is heavily sedated by putting the facehugger inside his body while it is very tiny and most likely to success with the payload? Keep in mind that the two other crew were completely pre-occupied with dealing with an adult Xenomorph running around the cargo lifter. They would not been in a position to be aware of David's actions.