If its one universe where any changes in the past alter the future, then the insta-second the villain left in the stolen time machine, his changes should have effected the present. They never would have even had a chance to stop him.
The "Time Patrol" series of SF stories by Poul Anderson addresses this problem by having the temporal police stationed at various dates throughout history. When some rogue operator changes the time line, those changes affect only those "downstream" from the change, i.e., living at later times in history. The changes do not affect the world "upstream," i.e., at earlier dates in history. This is true even for people living upstream who actually originated downstream and then time traveled, such as the Time Patrol members (this corollary is a little paradoxical, of course).
So, the Time Patrol's upstream cops receive a temporal alert about a change to the time line, and can go fix it. The downstream cops get swept up in the change and may wink out of existence entirely, depending on the magnitude of the change to the time line. They have to hope that their upstream colleagues will restore the old time line and bring them back to life.
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