Surviving reports from the initial uprising infer that the old movies we right. Any wound inflicted by a reanimate might be considered mortal, and lead to rapid death and than reanimation. However, more recent accounts seem to countermand these concepts.
In fact - we seem to lack any accounts of spontaneous reanimation. Numerous interviewees recall seeing former comrades reappearing a few days to weeks later, but none have seen the transition. Whether they were dragged down or killed by other means does not seem to matter. These sessions also note that reanimates have a tendency to clean the field of all bodies - theirs and fresh corpses, unless means are taken to prevent removal of the bodies. Cremation, or isolation in guarded compounds will work, but burial does not seem to deter them.
All due caution should still be expressed, of course. Given the lack of hygiene reanimates exhibit, any wounds they open are likely to be septic - but don't seem to spread the condition.
We have discussed several mundane explanations for this. The easiest would be to say the old reports are in error - made hastily, in fear, and thus prone to exaggeration. Or perhaps given the strange nature of the enemy, the error was deliberate - to help enforce a cautions mind set amongst those reading the reports. Standard procedure in a dangerous outbreak would presume someone is infected until proven otherwise for the safety of the responders.
More radically - it could be the incubation time is longer than the in field observation, or only affects those who die in short order after the wound. If desth is not immediate, the body eliminates the agent.
My personal hypothesis is that this has to do with the concentration of said agent. In the early days of plentiful hosts and fresh release - rapid reanimation was possible. Five years of environmental exposure and a geometric decrease in the number of potential carriers - the process has now changed. Either it is quite slow - taking weeks to months, or bodies must be brought to an area of higher concentration. Rather than casually passing on the disease, the reanimates must actually put effort into augmenting their numbers.
I do not have information on how this process might work, unfortunately. It may involve the rumored Type IV, or perhaps is subclass (following the standard nomenclature, a Delta.)