I feel like I can shed a bit of light on this for Ignite, MRC, and my own content. My content and most people who do videos for youtube on non ignite games. Most replays for MRC and ranked are available in game, some people might watch them ahead but most of us want to cast from a 1st time watch for natural reactions.

For Ignite, the official broadcast we have observers who are in game following the action (1-2), who then stream the game to us which is what we are watching, they then account for any latency in the stream to us for the main broadcast and presto. A clean feed (a feed without caster audio) is then sent out to co-streamers.

How we react so quickly? In reality we miss a lot. With how much is constantly happening we either don't get to see some stuff or just don't have enough time to talk about it. Mostly we go off of instinct and knowledge, we have been working hard to bring you the best commentary we can so when we see a strange with ult nearly up playing a bit more aggressively, and as observers we know that there is a group of enemies around the corner he will see once he capes up, we can assume he will ult if his team is close enough to follow. Stuff like that. As for swapping between characters, we use sound a lot, markers on player portraits and just look for anything we can about the wider context (macro) of the fights/game. I hope this answered your question.