Most of the primary sources from that time attributed it to Jewish well poisoining. When did the currently popular theory of the black death develop?
The Germ Theory of disease of course had not yet been developed at that time. It had to wait until the second half of the 19th century to get any scientific traction, and until a couple of decades into the 20th (when it saved the US's Panama Canal effort) before it became generally accepted.
The typical theory before then was that diseases were caused by Miasma ("bad air", or "malaria" if you were Italian). This led the advisors of Pope Clement VI to suggest he wait out the plague in a room surrounded by torches.
It appears to have been a team of scientists in 1894 investigating a Chinese outbreak from 30 years earlier who first identified Yersina Pestis. Historian Francis Gasquet appears to have been the initial champion for the idea that this was the same disease as the Black Plague, and (by 1908) that rats and fleas were the cause. The man had his detractors, but modern genetic studies of the remains of victims seem to back him up.
As an interesting aside, there was a period in the 19th century when people were getting increasingly sceptical of Miasma theory, but weren't sure what to replace it with. During this period we got the first effort I'm aware of to scientifically track down the source of an outbreak while it was occurring. It was for a Cholera outbreak in London, and the source ended up, in fact, being a "poisoned" (infected) well.*
* - Even more interesting, for you Game of Thrones fans, is that the scientist in question was named John Snow.
See Infection, Contagion, and Public Health in Late Medieval and Early Modern German Imperial Towns, by Annemarie Kinzelbach, published in Journal of the History of Medicine and Allied Sciences 61.3 (2006) 369-389
Abstract: From today's point of view, the concepts of "miasma" and "contagion" appear to be two mutually exclusive perceptions of the spread of epidemic diseases, and quite a number of historians have tried to discuss the history of public health and epidemic diseases in terms of a progression from the miasmic to the contagionist concept. More detailed local studies, however, indicate how extremely misleading it may be to separate such medical concepts and ideas from their actual historical context. The article presented here, based on local studies in late medieval and early modern imperial towns in southern Germany, demonstrates to what extent the inhabitants of these towns had notions of both "miasma" and "contagion." Furthermore, a contextual analysis of language shows that they did not see a necessity to strictly distinguish between these different concepts relating to the spread of diseases. Tracing the meaning of "infection" and "contagion," we find that these terms were used in connection with various diseases, and that a change in the use of the expressions does not necessarily imply a change of the corresponding notion. Moreover, a coexistence of differing perceptions cannot—as some historians have suggested—be attributed to a divergence between the academic medicine and the popular ideas of that period. A survey of measures and actions in the public health sector indicates that a coexistence of—from our point of view—inconsistent concepts helped the authorities as well as the individuals to find means of defense and consolation during all those crises caused by epidemic diseases—crises that occurred very frequently in these towns during the late medieval and early modern periods. As the article demonstrates, the interaction during such crises reveals the continuity of [End Page 369] ancient rituals and concepts as well as the adoption of new insights resulting from changes in the economical, political, scientific, religious, and social structures.
No brief summary can do this topic justice; you will find examples of isolation and techniques to avoid contagious diseases all through the late medieval and early modern period, long before the development of the germ theory of disease. The techniques used were not scientific, and often failed.
Plagues and Peoples covers some of this material in detail; a good read for those interested in this topic, and the historical effects of disease on civil society.
Note: You can find the above article online through your university library.