The parameters and hyper-parameters are dependent on the data. One way to proceed would be to ask the user to supply all the starting values. The other way is to use heuristics and default values to start with. JMP uses the second way because it reduces the burden placed upon users.
Different software developers and users might use different heuristics and default values for a given procedure. I think that such differences are moot because you can change the starting values to suit your preference or purpose.
In some procedures, JMP has used extensive research based on simulation to determine the best default values. There will still be cases where the default values are not appropriate or the best.