I'm not alarmed by those words nor the intent of a politician voicing those words.
I will be alarmed if those words mean abandoning the established path to citizenship (marriage or other, pay the "fees" wait, fill out papers, pay the "fees", wait, etc.) and less than desireable for the social/political health of the united States people are allowed to "become" citizens.
The article doesn't really address Paul's entire speech.
I read an article elsewhere about it, and he essentially agreed with you: their path to citizenship would be the same as for everyone else, and in line with everyone else. No short cuts, no fast track.
However, I still have questions about what he proposed to do in the interim. And, as I posted earlier, I don't think the border can ever be "secure".
any time you hear a politician say we need a “path to citizenship” they are advocating just that which you dread