Is there a way to keep Eraser from starting when Windows starts?
No, and that's by design. Eraser needs a running process for a number of reasons, the main one of which is so that it can co-exist better with UAC and other Windows security measures.
We are used to regarding programs that start with Windows with some suspicion; so many of them are not needed. Eraser is, perhaps, something of an exception; certainly, I see no sign on my systems (including an old, low spec XP laptop) that it is a resource hog.
The plan, as I understand it, is that with Version 6.2 the running process will become a service, thereby embedding Eraser within the system. If, like me, you think that this is something that should have been provided in Windows, this will be a welcome development.