Some questions and comments:
1. What kind of nonlinear model did you create? If it was a nonlinear ARX model (idnlarx), what estimation focus did you use? If you did not specify focus for nonlinear ARX model estimation, it defaults to "prediction" which estimates the parameters to minimize the 1-step head prediction error. Then, the 95% fit refers to the comparison of prediction results to the data. SIM cannot compute n-step ahead predicted response. For that, you will need to use the PREDICT command. Note that a good prediction model need not be a good simulation model. If you really want to create a model for best possible simulation results, use Focus = 'simulation' during estimation. In the GUI, this option would be available under "Algorithm Options" dialog.
If you are estimating a Hammerstein Wiener (idnlhw) or a nonlinear grey box (idnlgrey) model, then there is no difference between simulation and prediction models and you don't have to worry about setting the focus.
2. What initial conditions did you use for simulation? The results shown in the GUI are based on use of best (estimated) initial states that would maximize the fit tot data. The command that GUI uses is COMPARE which gives you several choices for handling initial conditions. When using SIM, the initial conditions that maximize the fit to data can be obtained using the FINDSTATES command (true for idnlhw and idnlgrey models).
For an idnalrx model, the initial conditions for computing the fit value are chosen such that they match the initial N samples exactly (N = sum of maximum delays in all regressors used by the model; see getDelayInfo, getreg). To reproduce those results, use sim(model, data, 'matching', data(1:N)). Here the first N samples of simulated response would necessarily match those of the data and the "true" simulation would begin from sample N+1 onwards.
