Managed to solve this issue, thank you for the suggestions.
As Anton Arhipov suggested I looked in the config center to see if the server I was deploying to was there, but it was not for some reason. I am not sure how Tomcat is configured on my machine but I think it has something to do with that.
I managed to get it to launch by adding the JRebel jar as a JVM parameter in my Tomcat settings similar to what Darius suggested. I did this by going to Window -> Preferences -> Tomcat -> JVM Settings and adding the parameter -javaagent:[Path to your jar]/jrebel.jar
to the "Append JVM Parameters" box. Now it successfully launches whenever I start Tomcat.