If I'm reading this correctly, the House ignored the bill the Senate had already passed (which had no funding for ICE) and passed a different version that includes $70 billion for Immigration and Customs Enforcement and Border Patrol.
NO.
The HOUSE (ONLY so far) has started a "2-part" (or rather, 2 separate votes) proicess.
The 1st "part" was that they FINALLY put the ORIGINAL bill passed by unanimous consent in the SENATE (that funded "everything in DHS but ICE/CBP) on the floor for a vote
AND passed THAT by a "voice vote" (no roll call vote) in the House.
The 2nd "part" was that the HOUSE (ONLY) passed
THEIR version of a reconciliation bill for ICE/CBP funding,
BUT that is THEIR version. The Senate hasn't passed anything associated with reconciliation and ICE/CBP yet.
The SENATE will most likely take the HOUSE (reconciliation) bill and modify it with Amendments (the infamous "vote-a-rama" ) and send it BACK to the HOUSE.
IOW, you need BOTH chambers to "tango to the same song" and they are not there yet.
ETA regarding this -
It sounds to me like this article overstates the House's "accomplishment" and plays down/ignores the implications of the fact that there are now TWO opposing bills, each one passed unanimously by one house of Congress. The article uses the words "resolving" and "resolved" in describing what the House did, but I don't see how anything been resolved, other than the GOP infighting that led to Johnson shutting down the House.
The HOUSE is supposed to "originate money bills" (NOT the Senate), and that is why they are the focus. However in the vast majority of cases (at least recently) the Senate takes a House money bill (or even some other unrelated bill that came from the House)
and will replace it as "An Amendment as a Substitute" with their OWN version and make the HOUSE pass that.