The NIV’s translation of among you who believed
suggests that the missionaries’ righteous conduct occurred in the Thessalonian believers’ midst, but did not relate to them in any particular way. It is more likely, though, that Paul wanted to indicate that he and his colleagues behaved toward the Thessalonian believers in a manner that was holy, righteous, and blameless. This is how most English translations understand the phrase, including ESV, NASB, NLT, and REB.
The Greek uses the dative case ὑμῖν/humin for you,
probably indicating toward
or for the benefit of.
1,2
It would have been more natural to use ἑν ὑμῖν/en humin to indicate among you.
10 You are witnesses, and God also, how holy and righteous and blameless was our conduct toward you believers.