Can you help with some math, more specifically calculating statistics?

Several days ago I was postulating that the efficacy of the Moderna vaccine might be inaccurate if it was tested in places with low infection rates. I know one place it was tested was where I live, and while the trial was happening there was a very low amount of cases here, so not very much chance to catch it. The person I was talking to said it wouldn’t matter since they used a placebo also, but I think it would. I am checking with the collective to see if I am thinking about this correctly.

It turns out that J&J was tested here also, but I think it was more recently and also J&J was tested in Latin America and South Africa where cases were high.

Yesterday I was watching TV and Gupta or Fauci (I cannot remember which) said similar to what I am saying that, J&J might have a lower efficacy rate, because they were tested in places with high infections.

So my question is, am I correct that if the infection rate in the community is very low, the efficacy rate of the vaccine might be overestimated?