I believe during said "Jump" Phase in the Primal Instances, that the Primals are technically under the Invulnerability status. That would be why the DoTs still tick but no damage is applied. If their DoTs and debuffs were reset between jumps then their buff stacks would leave too. Like if my Phlebotomize is at, say, 20s when I hit the primal, it jumps and leave the Targetable field for 12 seconds then returns, then my Phlebotomize DoT would be at 8s when it returned to the targetable filed. How ever it wouldn't have taken the missed 4 ticks of damage because of invulnerability during that sequence.

I tested it on Garuda HM during my Light Farming and, give or take some technical wording and programing jargon, that pretty much sums up the process in a nut shell. So by my observations the ticks still count but invulnerability prevents the damage.

Fun fact , if a limit break is over 80% cast (Give or take) when the "Jump" sequence happens, the damage still occurs as normal.