In the no chill method with cubes some brewers leave the hops in i.e They have not used a bag or hop spider and the hops get transferred into the cube while it cools overnight.
This obviously will leave the hops in from flameout temps down to cooling temps and the hops are in contact for longer. It is just like doing a hopstand for longer than a controlled method so the IBU's can creep up.
If you remove the hops then there are not any further hop contact its entirely up to you
which method you use but removal will give you more control of the bitterness.
Regards the beer not being bitter than normal with your method of bittering hops plus Whirlpool/Hopstand it is down to 2 things if you are using a recipe builder that takes Whirlpool/Hopstand IBU contribution in it then it will be calculated in the recipe builder and you will therefore have the IBU's that you wanted in the recipe. If you use a recipe builder that does not add IBU's for Whirlpool/Hopstands (some say no IBU's are created in Whirlpool/Hopstand)then that is when the beer can be more bitter than you expected, however a uplift in IBU's is not always as noticeable to everyone as some people are more susceptible to bittering taste than others