As many other posters have mentioned, this game is very scripted. Once you learn the script, it becomes much easier to anticipate what big moves are about to hit the table and how you can react to said big hits. There's a level of randomness in healing depending on how well the rest of the party is dodging the avoidable stuff that you will just need to deal with, but understanding the script will allow you to realize when you can heal and when you should be on your toes.
If you're having a lag problem (thus giving you less time to react) and you're playing on PC, there are programs like WTFast and Pingzapper that could potentially help alleviate that. I dunno if that's the case or not though.
