Could eggs/larvae have been deposited in plants or silt by birds or the pond's constructors?
While possible, I think this would be pretty unlikely, though there's a good chance this has happened somewhere sometime. Siren eggs aren't easily dislodged from the plants they're attached to, aren't very commonly found in the wild, and would probably have a hard time coming off the bird if they did get attached. While it's possible (and again, probable that this has happened somewhere), I think it would be an unlikely explaination for any given pond. Likewise, the bird could have carried the plants, but how often do birds carry pieces of water plants? Small clips are likely, but those pieces are much less likely to contain an egg, etc.
I'd think that floods would be the most likely explaination for siren migration. Ponds overfill, or channels of water appear and the animals swim through them, wind up in ditches, etc., and can disperse some distance. This can get them closer to the uninhabited pond, and then if the floods recede, some may be able to crawl short distances on land while there's still abundant surface water. Most will probably die (or aestivate and wait for the next flood; they might be able to leapfrog a bit if flooding is common) but some may be able to find a new source of water previously unconnected to water they'd be in before. It doesn't necessarily have to be in an actual flood plain, but one to two inches of water should be plenty for a siren to swim up. I'd imagine that any two bodies of water relatively close together would be at least partially connected during a heavy rain, since water generally heads in the same direction and runoffs are likely to meet somewhere downstream.
Of course, I'm not basing this on any actual research, just what I've seen in sirens. They really don't move very well on land and have no reason to leave the water on purpose. Amphiumas at least don't need to deal with gills as well, and do perfectly well out of water if necessary (such as when they're found above receded water nursing clutches.) And even amphiuma overland movement is pretty rare I think.