Misunderstanding document about leakage inductance in a flyback converter V2
Nevertheless, it seems if I correctly understand the document that Lp
  and Ll are not reversed just after opening the switch. So the current
  through Lp and Ll must grow up and this current is provided by Vin as
  the energy accumulated into the inductance is still growing up.


Your 2nd sentence is incorrect. The current can't grow. The current through the inductors now flows into the capacitor and its voltage rises at an initial rate governed by: -

$$I = C\dfrac{di}{dt}$$

Where \$I\$ is that initial current flowing though the inductors and now flowing in the capacitor called \$C_{lump}\$.


  Please tell me If i do a mistake


That's your first mistake as I see it so resolve that in your head and see if the rest of your confusion evaporates because I don't want to go through the rest in case your other comments/question are founded on this false premise.

I would also urge you to use a simulation tool in order to get a better picture of what is actually happening.