I just saw your update as I was about to post an answer, so you get it anyway.

Here’s some pics where it’s easier to see what’s going on with the mist net.

Different sizes of mesh are for catching different things. Too big and too many birds get through, too small and you’re catching too many things you don’t want and what you do want to catch will bounce off, so nets are sized and set up to catch a specific animal. Only catching what you’re after is going to minimize the chances to hurt anything right from the start. Proper vertical slack is given to make pockets in the netting of proper depth.

Birdy will hit the net and tumble down into the pocket and get feet, beak, wings caught up in the net and try to minimize movement. Care is taken to make sure they dont get caught near the ground/obstructions they could hit themselves on trying to get out. Nets should also be checked at least every 15 minutes, so nothing is stuck there longer than necessary.

Birds are removed by untangling them. If any are trapped together or in a situation injury may be more likely, they’ll be removed first.

I found a manual on using the nets with a lot more details for anyone interested in more specifics on how the nets work or more steps and advice for removing birds. Section 4 / Page 6 is where the good stuff starts, but I’d recommend at least skimming the whole 10 pages after, there is a lot of cool info.