Or perhaps by birds carrying seeds?
Not a chance. This movement was due to 19th century trade, not very long ago.
Unlikely-vanilla has been a trade item from the beginning-and although the beans/pods are fair-sized, the seeds inside are in a pulp-and tiny-they wouldn’t survive an ocean voyage in a bird’s digestive system...
Listen. In order to maintain air-speed velocity, a swallow needs to beat its wings forty-three times every second, right?
If a bird was to carry a vanilla orchid seed outside of its native range, it he plant would be unable to produce more seeds because vanilla requires a very particular pollinator that wouldn’t be present elsewhere.
That is why it has to be hand pollinated wherever else it is grown, such as in Madagascar and the Philippines.