Permission issue for Wordpress under Ubuntu

I’ve done a lot of research with the post already existing, but now I need some personal advise !

I’ve set up a Wordpress with the 1-click install, imported my Wordpress site. I then followed this tutorial https://www.digitalocean.com/community/tutorials/how-to-configure-secure-updates-and-installations-in-wordpress-on-ubuntu

I’ve check the permission on folders using the ls -l command. They are all « wp-user ». But if I check what user my wordpress run under, it’s « www-data ».

I can’t upload media via the Wordpress interface, also can’t remove certain extension… looks like a permission issue, if I change the upload folder to 777, it works. Should Wordpress run under « wp-user » instead of « www-data » ?

Thanks for your help and clear answer (i’m not a pro ! ;-))