Robert,
The inter-arrival times for the events in a Poisson process follow a negative-exponential distribution. The ExponentialDistribution object implements this distribution in JaamSim.
Do you want to actually sample a Poisson distribution? We haven't implemented any of the discrete distributions such as Poisson, Binomial, etc. simply because we couldn't think of a use case. If this is what you need, you can calculate the probabilities for each outcome from a Poisson distribution and enter them in a DiscreteDistribution.
Harry