Arms Race - Level Up when killing specific people
Solution 1:
You are correct in the two ways you've mentioned on how to level up, your question arises from missing the third way to level up.
The three ways to level up in Arms Race are:
- Get 2 kills with a weapon
- Get a knife kill
- Kill the enemy leader
So the certain people would have been the enemy leader, which would level you up to the next weapon with a single kill on your weapon.
The Team Leaders can be easily seen in the mini scoreboard at the top of the hud:
The CT leader will have a blue border around their icon and similarly the T leader will have a yellow border.