Oh right, I have most of the frequently-negative posters blocked at this point and didn't notice your previous post.
As for "rift travelling through time", that seems like mixed terms. My understanding (though I could be wrong) is that time travel is Alexander's domain while Omega has the ability to manipulate the dimensional rift, and between them they provided the basis for what the time machine needed to be capable of.
When we time-travel with Alexander it isn't shown to resemble the rift when we use it. The only time that time travel looks like the rift is when Elidibus somehow altered the Ocular portal into a time-portal, and we haven't seen another use of that type of time travel. It's possible that Elidibus devised a further method incorporating both beings' abilities.
Additionally, the Exarch's boast-speech to Emet seemed to list them as two separate things. I don't have the exact quote but it was along the lines of "we tamed the wings of time and grasped the true nature of the rift". One part for Alexander and one part for Omega. It's still somewhat ambiguous maybe, if I've got the words right, but still that's how I took it. Probably also based on the notes in the Twinning.