Difference between LTI and transfer function block

I have a first order transfer function of the form :

and I know its output form for a step input

I tried impleneting it using transfer function block in simulink with a step input, and didn't get the expected result

But, when implementing it using the LTI block I got the exepected reuslt.

My question is, why the outputs are different, shouldn't they be the same since the trasnfer function can also represent an LTI system?

Thank you

[Paul]

Can you provide more details explaining exactly what you tried. I see identical output from from the LTI block and the Transfer Function block for a0 = 1 and b0 = 2.