I think your understanding of the Read The Bill Act is correct.
It was first started, as I understand it, by DownSizeDC.org (Harry Browne was one of the three founders). They wrote a sample bill (I don't know how much Rand Paul's version differs) and in that sample the summary states:
To require a Constitutional Authority Statement in support of every bill or resolution, the verbatim inclusion in each bill or resolution the text of any existing law amended, and, before final passage of any bill (other than a private bill) or resolution, the full verbatim reading of the text to each house of Congress called to order with a quorum physically assembled throughout, the verbatim publication of every such Bill on an official Internet web site of the Senate and the House of Representatives before final passage of any Bill in each house of Congress, prior notice of the calendar week on which the final vote is scheduled to be taken, the execution of an affidavit by every member of each house of Congress attesting that, prior to voting for passage of a bill the individual member had either listened attentively to the reading of said bill or had personally read it in its entirety; and to provide for enforcement of the printing, reading, entry, publication, recording and affidavit requirements herein.
So, yes. Enough members have to physically have their butts in the seats and listen to the full text of the bill being read verbatim and outloud - no summaries. And to sign an affidavit so attesting. (I think that the affidavit should be attached to a felony offense for a false signing saying they were there when they weren't and that no one can vote on that bill who hasn't signed.)
There is no way that many of the bills they sign could be read in the time they could stay seated (like ObamaCare or the Defense Appropriations bill). I like the idea of bills that are no longer than a quorum of congress' attention span :-) Some people might say that this would reduce the number of bills that congress could pass in a year. Excellent! I'd consider that an added benefit.
This sample bill is about 3,111 words in length, so at somewhere between 100 and 200 words per minute, it could be read out loud at in less than half and hour. If you try to read the Defense Appropriations bill or ObamaCare, not only would it take more time than is remotely possible, those two couldn't be read, no matter at what speed, in a way that made them comprehensible. Imagine the CSPAN showing of that attempt!
There are other aspects of some of the proposed transparency acts that relate to how a version has to be put on the internet 7 of days before the vote and to be identical to what is voted on.