No. That's a complete misreading by the media.
It is a crime to seek asylum outside designated US entry points. You can't tramp across the desert and then cry "asylum". You can only request asylum at official border crossings.
Somehow that fact is getting mixed up in some reports which imply that the criminals will be held outside our borders. I don't think so, but I would love to be corrected if I'm wrong.
“It is a crime to seek asylum outside designated US entry points.”
They can legally seek asylum anywhere, I believe.
“The contracting states shall not....impose penalties on refugees who entered illegally in search of asylum if they present themselves (Article 31)”
https://en.wikipedia.org/wiki/Convention_Relating_to_the_Status_of_Refugees
They have a duty to seek it in the first available country, i.e. Mexico, I believe.
A refugee is
“A person who owing to a well-founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group or political opinion, is outside the country of his nationality and is unable or, owing to such fear, is unwilling to avail himself of the protection of that country; or who, not having a nationality and being outside the country of his former habitual residence as a result of such events, is unable or, owing to such fear, is unwilling to return to it.”
None of these people are refugees.