You appear to be having some negative transfer issues moving from Minitab to JMP. The issue you seem to be having an issue with is that in Minitab, If a graph is open in Minitab, and you close the session, when you reopen the Minitab project, the graph will be regenerated. In JMP, if you have the preference set to save your current session when you close JMP, the graphs will be regenerated automatically when you start the session up again. This is set under the General tab under the pull down menu
File==>Preferences
One of the real advantages in JMP, is the ability to save the scripts from the different analysis platforms that one runs. If you save them to the data table, and then save that data table, you will always have them available in the future. When you reopen that table, you can rerun any of the applications you ran by simply clicking on the saved script. This is a very powerful feature.
Jim