If your death occurred when the cougar pounced and mauled you then yes, I believe it is. I am pretty sure the cougar/panther pounce attack and the bear maul attack are scripted deaths and the unlimited health option does not protect against scripted death.
Mouse over feature is when you're in your satchel/inventory. Whatever item you are currently hovering over or selected will show the value you have in the trainer. Change value and close and reopen satchel and the modded total item will appear.
Example: your hovering over apples, you have 1.modify value to 99 via trainer, go back to game and you now have 99 apples.