Firstly, feedback itself is a tool that should only be used to "fine tune" learners' understanding. It is not a replacement for instruction. Unfortunately, insufficient effective instruction* occurs in typical EFL/ESL classrooms & I suspect that much of the research into corrective feedback in second & foreign language learning hasn't taken this principle into consideration so the results have been very mixed, & so I'd say that the controversies that surround the debate on corrective feedback are from poor quality evidence more than anything else.
Rod Ellis offers a typography of feedback here: https://academic.oup.com/eltj/article/63/2/97/440749
The type of feedback you've described is known as a "recast." They may be effective but only if your conversation partner (1) understands your intentions (to give corrective feedback), & (2) processes the feedback, which means switching attention from the topic of conversation to attend to the feedback, & (3) he is "ready" to learn/correct that particular linguistic feature in the feedback, i.e. It's at the right level for them to understand.
On the downside, some researchers have argued that corrective feedback can cause learners to simplify their speech in order to avoid making errors & that this may restrict their language development. The argument is that "interlanguage" development (AKA "developmental sequences") includes errors which are unavoidable & a natural part of the process & that they are insensitive to instruction. Giving corrective feedback may discourage learners from persisting in these areas of development (making errors), with negative consequences.
* "effective instruction" is also a controversial topic in language learning research but it is clear that the usual grammar translation, drilling, & pattern practice exercises have little effect on language learning in terms of getting better at communication (developing communicative competence). One promising avenue of research on language instruction is in "Structured Input" (Bill vanPatten), explanation: https://www.youtube.com/watch?v=LIAhI5oEgHE&list=PLCvyUoftI84sWQ6QCFrPweda0Cwf49SJK&index=4