Can the freshness of butter affect taste of cooking?
Butter can/will turn rancid if not stored properly; using rancid butter will completely destroy a recipe as it will have a strong smell and taste; probably why people use ghee instead of butter; smell it before using it.
In that particular recipe, I would imagine using more butter will not change much in term of taste or texture; unless you really messed up measurements from 2tsps.
This would be somewhat impossible to explain, adding butter will add more fat and some additional unctuosity to a dish; in that case, I imagine not much change will happen since there is also a lot of water and the cashew paste in the recipe.
As in any recipe, using fresh ingredient is the key to making a recipe work; even fats like butter or oils.


To keep butter fresh as long as possible: 


Buy only what you need (if you cannot store it properly)
Keep it cold in the refrigerator. (and properly wrapped).
Freeze unused butter (cut it in smaller chunks before, so you can only take out small amount at a time).
Use a butter "bell" that will keep the butter in water (don't forget to change water regularly).