“If someone needs internet for parnassah or school, they should use it for that and no more.”
Easier said than done. This is the entire argument of the anti-internet rabbonim- that some access will lead to temptation and addiction.
People that use the internet for parnassah often need to be on it for long periods of time answering emails, writing documents or doing whatever. However, they also have some amount of free time where they can do what they want. This timeframe is what emunas yisrael is marketing to.
I don’t think the Rav would ask those who are directly ignoring the peak not to- wouldn’t he think they’ve already gone too far off to be helped? It makes more sense that the site is aimed at people who have a heter to use it, since that would make the Rav more comfortable that only they are on it, I assume.