Safari login Mobile not working everytime

Hey there,
On iPhone, this following case uses to happen often:

– I ask to be logged with Facebook (clicking on the FB button from this plugin)
– The FB popup opens, I enter my FB email and password
– The FB app tells me to continue (And that I have already used this app before)
– But then I am redirected to the first login page of my website as nothing was happening, and I am not logged to my account.

I have found this video that explains the problem perfectly. It is not the same technology but exactly same issue.

Any help?
Thanks!!