I don't know what is causing your issue exactly but I think it would have to be something to do with your signal from your ps4 to the server where you're lagging out like that. The issue could be on SE's end, I play on ps4 and I haven't had this issue. Before I upgraded to the ps4 I was on the ps3 and on occasion had the issue.

Problems like this have occurred with SE in the past and seems to bounce around between individual accounts. Contact SE to report a big and explain you had your internet checked and that your lag issues are not anywhere on your end, also tell them other online games work and run perfectly fine. I've had to do this in the past with ff XIV as well as on ff XI