Since you are only getting to the point where you swap tanks and healers once, the tank that starts on Nezir will take significantly more damage. This is two fold. First, Nezir does more damage to the tank normally because of the stacking debuff. Second, immediately following Anshal's ultimate he has a 15 second buff to his damage and that is the only time his tank damage gets to be extreme. So if you start on Nezir's platform, you have to take the heavier damage from the start and are the first tank to have to deal with Anshal's buffed damage. The other tank won't experience that until they switch back for the second ultimate.
I'd say your damage isn't that out of the ordinary. Though positioning plays a bit in this encounter. For example, since Anshal gets a buff from his ultimate for 15 seconds, if you aren't standing right next to him and let him meander over to you that wastes some of the buff duration before he actually hits you. On Nezir's platform, healing is significantly lowered if your healer is also getting out of the frost patches quickly and also making sure they aren't in the same line as you for when the cone attack occurs.
It doesn't really look like anything out of the ordinary really other than the fact that on the second attempt your DK tank took no damage at all from Nezir (did a switch ever occur in that case)?
"In anything, if you want to go from just a beginner to a pro, you need a montage." /w TankSpot WTB Montage for Raiders.