There are a few different types of intervals shown:
I believe that all of them are 95% intervals.
You can read some information on the different intervals in the documentation for Reliability Forecast: The Reliability Forecast Report.
However, there are details missing, so I will try to get them added to the documentation in the future. peng.liu might also be able to help further describe the different intervals (beyond what is available in the documentation).
Here is additional insight that may help.
In the JMP Forecast platform, you have the option for two interval options. These are found in the red triangle next to the Forecast section of the report. The two options include Plug-in Interval and Prediction Interval. Plug-in interval option is a "Confidence" interval and is non-simulated. Plug-in interval does not consider uncertainties in parameter estimates, and use random Poisson variable to approximate the count in a time interval instead of sum of random Binomial variables. Prediction Interval is a “Prediction” interval with three options that can be found in the same red triangle called Prediction Interval Settings. This type of interval considers uncertainties in parameter estimates. Here you have the option of Approximate Distribution Option which uses a random Poisson variables to approximate the count in a time interval, this is generally much faster than but as accurate as using sum of random Binomial variables. To use sum of Binomials, turn off Approximate Distribution option. You can also select the Random Seed option or the Monte Carlo option if you want to generate the same results each time.
The confidence level is 95%