a little bit familiar:)
System Identification Toolbox lets you identify transfer functions and other models from input-output test data. "Input data" means the excitation signal you apply to the system, not the time vector you use. Step response by definition means system response to step input, so the input signal is 0 at time 0 and then is equal to 1.
So to get the results you expect:
u=ones(size(t));
Then import u and y (not t and y)as input and output data, starting time:0, sampling time: t(2)-t(1).
Then estimate a transfer function, and you will get your 1/(s+1).
