Does the second death have power over believers?
No. Revelation 20:6 states that blessed and holy is the one who has part in the first resurrection, and over such the second death hath no power. That first resurrection includes believers from Adam through the end of the tribulation, so the second death has no authority over them.
Les teaches from Revelation chapter 20 that the first resurrection is only believers, from Adam clear down to the end of the tribulation. In contrast, the rest of the dead—the lost who have not experienced resurrection—do not live again until the thousand years are finished, when the great white throne comes about. For the believer who has part in the first resurrection, the next words are that the second death hath no power.
Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.