Paul was simply saying that "When the Lord Jesus shall be revealed from heaven, with his mighty angels, in flaming fire taking vengeance on them that know not God and that obey not the gospel of our Lord Jesus Christ" - then the Christians alive at that time will marvel at seeing Christ (verses 7 to 8).
In verses 4 to 7 Paul knew about the tribulations and persecutions those Christians in Thessalonica had already endured. He said it was righteous for God to recompense tribulation to those who troubled them. That would happen at Christ's glorious return, with the angels, for the Day of Judgment and Resurrection. All the Christians in the first century expected that could happen at any time. They did not know when Christ would return, but they had total faith in his promise that he would.
You ask explicitly what the last phrase means: “for our testimony to you was believed.”? It was the testimony of Paul and the Apostles that the crucified Christ was raised from the dead, ascending to Heaven, from when he would return one day for that spectacular Day of Judgment and Resurrection. They believed that they would be caught up to join Christ in the sky, where the dead in Christ had just gone.
Paul had earlier written to them about that, in his first letter to them. Read that in 1 Thess. 4:13 to 5:6. In part, Paul said:
"For if we believe that Jesus died and rose again, even so them also
which sleep in Jesus will God bring with him... we which are alive and
remain unto the coming of the Lord shall not prevent them which are
asleep. For the Lord himself shall descend from heaven with a shout,
with the voice of the archangel, and with the trump of God: and the
dead in Christ shall rise first: then we which are alive and remain
shall be caught up together with them in the clouds, to meet the Lord
in the air, and so shall we ever be with the Lord." - A.V.
For nearly 2,000 years now, that glorious Day of wonder and admiration awaits. We still do not know when it will suddenly happen but we are to be prepared with the same strong faith and expectation that those first century Thessalonians had. Our wonder and admiration in the appearing of our Saviour with hosts of angels will know no bounds, whether we are still alive on Earth when it happens, or whether we will have died by then and so have the honour of being with Christ at his return, clothed with resurrected bodies.
This has to be believed by all who have faith in the return of Christ. We today who are Christians believe the same testimony of Paul and the Apostles, otherwise we cannot call ourselves Christians, nor will we be thrilled at Christ's coming for and with the saints - those who do not believe that testimony will be terrified, as Revelation 1:7 says.
It is not necessary to wander into interpretations of end times to answer this question, for you simply ask what the logic is in that one verse. The logic becomes apparent when we read what Paul had previously written to them on that subject, and tie it in with his further information about how amazed they will be to see Christ and the angels, not to mention Christians who had died previously.