Don't go stressing yourself out in trying to "save" people who pull first because if you're healing them then you'll get aggro and die a lot faster than that DPS who ran in like a Leeroy, and if it's the healer doing the pulls well then... your cure 2's can only heal you so much but give a few seconds with half a dozen mobs critting and doing their special moves on you and you'll be eating mud pie and only have yourself to blame for it and not the tank who is staring at you and wondering did your brain cells forget to resurrect with the rest of you the last time you KO'd.
On the other hand I know tanks who've rushed so far ahead of the party and try to kite pull a dozen mobs at once and expect the healer to keep them alive, either they've kited too far from the healer that they're already half-dead by the time they stop kiting or they're taking more damage than the healer can cure.