Why do you think that the advent of the telegraph motivated the use of a more secure cipher like the Vigenère cipher?
Prior to the telegraph, much of the communication was done so through hand written or typed correspondence. There was a sense of privacy when communicating through letters because they are sealed and it was assumed that only the intended recipient would read them. For people communicating more sensitive information, there was a chance that someone would intercept the letter and so enciphering it was standard in this case. The telegraph had the advantage of speed over the letter and so communication through telegraph was more favorable. However, a telegraph operator always reads the message when communicating via telegraph and so there is a decrease in privacy when using this system. This decrease in privacy could have been a motivation to use more secure ciphers like the Vigenère cipher. The only thing hindering people from using the Vigenère cipher over the Caesar cipher was the complexity and the amount of effort needed to implement the cipher. When there became a further decrease in privacy while using telegraphs, people may have realized that the extra effort needed to use the Vigenère cipher was worth it if it meant more privacy.
I think this can be seen presently with the advent of the Internet. The amount of privacy we have decreases when communicating through the Internet. To regain this privacy we do things like encrypt our data through the use of VPNs or by browsing websites that utilize SSL. A decrease in privacy because of the Internet has prompted us to go an extra step to regain it, and so it makes sense that the people that lived during the advent of the telegraph had done so as well.