There are two basic problems with the suggested procedure, structural and appearance.
The tread nosing (the outer edge of the step) is the most vulnerable part of the stair. This small over-hanging edge is where most of traffic load is concentrated, and it is where most of the impact occurs. Joining concrete in such weak-point area is not recommended, even if special measures when joining concrete subjected to stresses, such as placement of steel dowels (to resist tensional stresses which the concrete by itself cannot resist), special bonding agents, and most importantly, the areas to be joined should be large enough to enable the new and old concrete to hold together. Because of the small size of the added part and the concentrated stresses such measures are not practical and cannot be properly applied to the step nosing.
The second aspect is an aesthetic one. The joint between the old concrete and the new cannot be fully concealed. It will always have a 'line' and the colors will not fully match.
Making a mistake in the size of step by 2 inches is in my opinion a serious one, and you should not accept anything short of replacement the entire stair.
Hope this helps and good luck.
I see. So he intends to pour concrete using vertical forms covering the entire 7" height of each step, at a distance of 2" away from where the old edge used to be. If that is the case, then it should be ok, provided:
If he follows the above procedure, you should be ok. Otherwise, like I said before, this is not just an oversight or a simple mistake in dimensions. It is indeed a serious one and he should fix it to your complete satisfaction.
Please let me know if you need further assistance.