Brian is, I believe, confusing the end of this eon (which leads up to the commencement of Christ’s reign) with the end of the next eon (during which Christ will be reigning). The eon in which we're living is going to end after the final seven years prophesied in Daniel 9 have transpired (which will end just before Christ returns to earth). And the next eon (the “coming eon” or “age to come”) is going to end sometime after the thousand years referred to in Rev. 20:4-6 have run their course, and the insurrection prophesied in Rev. 20:7-9 has occurred (see Ezekiel 38-39 for a more detailed description of the events referred to in Rev. 20:7-9). When this event takes place, the saints will have already been reigning with Christ on the earth for a thousand years.
Addendum (added 2/22/20)
Another chronological problem with Brian’s position involves the timing of when Satan is cast out of heaven and into the earth (as described in Rev. 12:7-12). At the beginning of this rebuttal I quoted Brian as stating, “When we’re removed, Satan will be cast down and bound for a thousand years and released for a short time during the end of the thousand-year period, where he will set off the events described in Matthew 24, including the abomination of desolation in the temple.”
The problem with this view is that Satan’s involvement in the events described in Matthew 24 is going to take place immediately after he is cast down from heaven. In Revelation 12:13 we read, “And when the dragon perceived that it was cast into the earth, it persecutes the woman who brought forth the male.” This persecution of “the woman” by “the dragon” refers to Satan’s persecution of the believing Jewish remnant who will be living in the land of Israel when the abomination of desolation takes place, and will begin to be fulfilled at the start of the 3 ½ years of “great affliction” referred to in Matt. 24:15-22 (when, after perceiving the abomination of desolation standing in the holy place, the remnant in Judea flees into the mountains/wilderness to be protected for 1,260 days; cf. Rev. 12:6, 14-17).