Hello, everybody.

My group and I had our first few games of Infiltration today, and we just couldn't decide how Nelson affects the game. Does he increase the alarm level each round even if there aren't any operatives in his room?

Yes, he does. The alarm portion of the text is not conditional on the first.

For further details, see Cards with Multiple Effects on page 10 of the manual.

edit: Or I can just post it here for you.

(note: though this only specifically lists item cards, the spirit of this rule is carried throughout the game)

Cards with Multiple Effects
Many item cards such as “Data Code Breaker” allow an operative to play
and resolve additional action or item cards. An operative must resolve each
effect in the order listed on the card, if able. However, if an operative cannot
resolve one of the effects, he may still resolve other effects on the card.
For example, “Data Code Breaker” reads: “Destroy 1 tech lock in your
current room. Then play your ‘Interface’ card.” If there is no tech lock to
destroy when this card is resolved, the operative can still play and resolve
his “Interface” card

Alright, I see. Came to this conclusion myself today during a game.

Thanks for the effort and help!