And if "they" didn't say anything, the question would hang over them. Also, what @Greg Cox said.
I don’t think so. If TPTB never said what universe DSC was set in, there’s no way anyone would think it was set in the prime universe of TOS. At worst they’d think it was set in the Abramsverse.
All I’m saying is that at a fundamental level, I really don’t see people thinking this show is set ten years before TOS if it wasn’t told to them that it was. But that’s just my opinion.