It was due to the Restrictions option I used to block adult websites. By turning it off I could enable Adguard Pro and turn back my restrictions on again.
However what is strange is that I did not face this issue with Adguard regular version. Something I cannot explain.
Because I had some issue to activate Adguard Pro (cf. my previous post) I went through the issue and review my setup. I do not know exactly what I did to make it work but the ad now disappears at the launch of the application. You make my day!
I love this new Adguard Pro version. Even if I paid a lifetime Premium account I had no issue to pay the extra 0.99$. To be honest I will have paid 2$ for it. You did a great job! Keep the good work going!