There's also the thought that evolutionary adaptations are so tightly coupled with environmental landscape that it'd primarily work the other way around. For whatever defense mechanism we lack for that particular parasite, they lack
anything to combat their own million-year-more-efficient predators (like our immune system). It is less about evolution moving forward and being more 'advanced', and more about evolution ensuring an efficient equilibrium with a crazy-dynamic environment. Jumping into a new environment after being conditioned for a very different one likely leads to death much much more often than an accidental advantage. You might not be able to even breathe were you transported a few hundred million years either forward or backward.
Depending on how far back you go, today's planetary environment is a very different place - in terms of chemical food, predatory tactics, biochemical efficiency, atmosphere, etc. Having to compete against organisms that are efficiently adapted in our current environment will almost certainly be immediately lethal for these revived organisms.