There are few importants things to know to properly hook the Profiler on different platforms.
In order to properly attach the profile, "Build and Run" button from the Build Settings window with the option Autoconnect Profiler checked must be used.
Another mandatory option, in Android Player Settings inspector in the Other Settings tab, there is a checkbox Enable Internal profiler which needs to be checked so LogCat will output profiler info.
Using only "Build" will not allow the profiler to connect to an Android device because the "Build and Run" use specific command line arguments to start it with LogCat.
In order to properly attach the profile, "Build and Run" button from the Build Settings window with the option Autoconnect Profiler checked must be used on the first run.
On iOS, there is no option in player settings that must be set for the Profiler to be enable. It should work out of the box.