Why haven't alternate-stream time travellers begun appearing?

I lack the mathematical background to understand quantum physics on anything but the most basic level, so please excuse me if this sounds odd.

As I understand it, it’s entirely possible to travel backwards in time, and in fact I recall seeing a mathematical proof published in SciAm some years ago, although I couldn’t understand all the Greek symbols. There is no paradox so long as, when you travel temporally, you never land in the same stream from which you originated. That is, assuming the Everett-Wheeler “many worlds” model, so long as one travels to a different “branch” of the probability tree, no physical or mathematical law has been violated.

The actual method of time travel has been understood for some time. Because time and space are simply different ways of looking at the same phenomenon, one can bend space to bend time, and vice versa. So using a powerful electromagnetic field to bend light entirely in a circle creates what is, in essence, a time machine—but one capable of travelling back no further than the moment when it is switched on. In fact, there is a theory that the instant one of these is constructed, we will begin receiving messages from an alternate-stream future.

So far so good. Now, my question is, given that we know it is physically possible to construct a time machine, and given that everything which can physically occur, does, in some alternate probability stream, why hasn’t an alternate probability stream where we have constructed one of these time machines begin sending people back to us? Does the bent-light time machine have to have a terminus in our specific branch? Does this mean that the instant we construct one, we may get flooded with travellers from billions of possible future branches? Given that everything which is possible will occur in some branch or other (amd will not in others) how do we know whether or not we are currently in a branch where this will occur?

(And on a slightly less General-ish note, what do you believe the political effects will be when several hundred million time travellers from every possible future begin appearing around a research lab somewhere?)