Then, the Lord will send his angels to gather his elect. It is done at the sound of a great trumpet. 1 Corinthians 15 tells what trump it is:
51 Behold, I show you a mystery; We shall not all sleep, but we shall all be changed, 52 In a moment, in the twinkling of an eye, at the last trumpet; for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
So, it happens at the last trumpet. The simplest place to find a last trumpet is in the book of Revelation, where seven trumpets are referred to. Let us see what is said there about the seventh trumpet. In Revelation 11, we find:
15 And the seventh angel sounded; and there were great voices in heaven, saying, The kingdoms of this world are become the kingdoms of our Lord, and of his Christ; and he will reign for ever and ever.
16 And the four and twenty elders, who sat before God on their seats, fell upon their faces, and worshiped God,
17 Saying, We give thee thanks, O Lord God Almighty, who art, and wast, and art to come; because thou hast taken to thee thy great power, and hast reigned.
18 And the nations were angry, and thy wrath is come, and the time of the dead, that they should be judged, and that thou shouldest give reward to thy servants the prophets, and to the saints, and them that fear thy name, small and great; and shouldest destroy them who destroy the earth.
19 And the temple of God was opened in heaven, and there was seen in his temple the ark of his testament: and there were lightnings, and voices, and thunderings, and an earthquake, and great hail.
Now, it is clear here that the wrath of God begins at the point of the sounding of the seventh trump. That is clearly testified to in verse 18. God's wrath is not spoken of prior to this point, and scripture requires that the church must leave prior to the outpouring of God's wrath.
1 Thess 5:9 For God hath not appointed us to wrath, but to obtain salvation by our Lord Jesus Christ.
So, it is clear that here, at the sounding of this seventh, last trump, is where the rapture of the church and the gathering together with our Lord appears.
Following this, the vials are poured out. These are found in Revelation 15.
1 And I saw another sign in heaven, great and marvellous, seven angels having the seven last plagues; for in them is filled up the wrath of God.
This is the wrath we are spared from. It occurs at the right time, just following the sounding of the last trumpet. This is when Jesus said it would happen.
Another possibility is that the vials and the trumpets coincide. The trumpets are 1/3's..... the vials are total. But look at the vials carefully. Not one of them will hurt a believer (Rev 16:2 - only those who have the mark; 16:9 - God has total control; 16:10 - beast's kingdom plunged into darkness; 16:18 - 7th vial is like 11:19 - the 7th trumpet). This protection does not necessarily require the removal of the believer from Earth.