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Most SPICE programs use ideal parts. Often if is possible to add in the imperfections found in the real world.
Most transformers and inductors in electronics simulation programs do not saturate. They will function at 1,000,000s of amps with no problem. A real transformer will saturate and maybe explode.
I do not fully understand your question. If you have a saturation transformer or inductor in SPICE, it has a inductance at low current. At the saturation point the inductance drops to very low. (saturation happens when the (voltage x time) or the (current) is too high.
You are reading too much into the proteus simulator... In the list of transformers you have pairs.. Ideal and saturated... One will simulate saturation and one wont.. If you list the properties, all the relevant windings, current, inductance, can all be tuned to your specific needs.. If you allow too much current, the simulator will show you the "real" simulation..