This sounds a lot like [How do I drug a population in the most efficient way?][0].

The main problem I see is that radiation just doesn't work that way.  To my best knowledge, you cannot create a "special kind" of radiation that will cause particular mutations.  You can limit the effect to certain cells by only irradiating those, but most mutations will still not be very effective.  Decreasing the power won't make it any more effective; it'll just make both harmful and non-harmful mutations less common.

Disregarding that, my suggestion would be to put it in the water.  It's the easiest place to rapidly start adding a substance to, either by adding something to the wells or modifying the rain (if you have the technology).  In a case like this, you can get the radiation to become fairly insignificant by the time humans can measure it by choosing an isotope with a [suitable half-life][1].  Water with [Tritium][2], refreshed every five or so years, could work wonders on your population.

Alternatively, you could make a whole in the ozone layer.  That would increase radiation, and people at that time would likely notice little else than "being in the sun makes you sick".  I am not sure what would have to be done to recover it later.

For the "thousands years in advance" part, you're going to have some logistic issues.  Robots that manufacture and distribute whatever it is you need and then self-destruct are probably the best option.

As an alternative that takes that into account, they could have launched a spaceship containing a radioactive compounds at speeds near that of light.  If it were to keep going at that speed and crash back into the Earth, far less time will have passed for it than for the planet, which would mean that rapidly-decaying particles wouldn't have decayed yet.  This could then be written off by the Romans as a meteorite impact.

 [0]: https://worldbuilding.stackexchange.com/q/843/2428
 [1]: http://en.wikipedia.org/wiki/List_of_radioactive_isotopes_by_half-life#109_seconds
 [2]: http://en.wikipedia.org/wiki/Tritium