I have not seen NT-H1 do that, and I've used NT-H1 in situations all the way up to 105°C.I've never seen a paste do that before. Have you?
There isn't anything special about sitting on the CPU die when it comes to temperature, so I am surprised you observed the separation.
I wonder if you have a potentially bad tube of NT-H1? Is it old? (>6 months)
Long ago, like 4yrs ago, I had a 2yr old tube of AS5 that had separated on me from sitting on the shelf for so long. I went to put some on my IHS and a bunch of liquid squirted out, reminded me of when I don't shake ketchup bottle when it has been sitting for a while.
But after 2yrs I imagine just about any TIM will separate under the influence of gravity as these pastes are all emulsions. That doesn't explain why yours separates in a matter of months and after application, head-scratcher there.