How do beam weapons damage enemy crew?

Do I need to draw the beam directly across the enemy crew member, i.e. exactly over where they are stood, or does just damaging the room they are in also hurt any crew in that room?

Based on observation, both sorts of beams behave the same way. Crew members are only damaged in the path of the beam. It's hard to test this as you only see health bars right after a hit, and sometimes yhou need to follow up with another weapon and try to eyeball the results. I thought I had confirmed that regular beams damaged crew members regardless, but I just did some more testing and it seems I was mistaken.

Bio-beam definitely does not hurt crew people not directly in the path.

I was curious about this as well.
Having run with full sensors and very carefully taken out a ships air supply,
it was fairly easy to test.

Beam weapons must cross the hit-box of units in order to do damage to them.
This applies to all beams that can harm units.

As an extra note, the beam must cross where the unit is at the time,
if the unit moves out of the way in time, you are out of luck.

Beam damage is inflicted to crew depending on room's squares.
Every room in FTL is divided in two or four squares, each contain up to one crew and one hostile crew. When a beam first hits a square, the beam damage is instantly attributed to each crew in it, hostile or not.
The uses that result from this are the following :

• You can't hit all four crew stuffed in a large room at once
• You have to aim not just for a room, but the part of the room crew is situated (can be known with sensors or knowing ships layouts)
• Actually you have to aim not where the crew is currently situated, but where it'll be when beam hits, each beam having a different speed and crew also moving notably to repair systems
• With good timing and anticipation you can combine those and hit twice a crew as they move across squares. The crew needs to be near the end of the square when the beam hits, and go through the boundary before the beam catches up.

I'm still doing some testing, it's possible this last behaviour only happens when crossing a door.