What happens when you killing a Monster only to have to face a new Wandering Monster?

[Clipper]

Yep, notice that the box on the first page of the rules that lists the rules that can't be broken unless explicitly stated on a card include:

3. You cannot collect rewards for defeating a monster (e.g., Treasure, levels) in the middle of a combat. You must finish the fight before gaining any rewards.

In this case, you didn't finish the fight by beating the first monster. The fight was continued by the addition of the second monster. Thus, you don't get any rewards, as per the above rule.