I ALWAYS add a few TBSP instant pudding mix to my cake ingredients- whether using a mix that has pudding added or a scratch recipe. I also measure the water or milk (I usually use milk in place of water) & oil GENEROUSLY- adding probably an additional TBSP of each. Too much oil and the cake realy tastes oily though, so don't over do.
My thoughts are that even if the pudding mix doesn't add additional moisture I think it must help hold onto the moisture during the baking process.
By substituting milk for water you are adding more fat to the mixture also, which will help moisten. In a very delicate recipe- I only sub out half the water for milk because you don't want to mess with the fat ratio too much, but in most recipes I have not found this to be a problem.