They both work and have different usages. "At" marks a specific time, "in" indicates within a duration of time. We came home at the same time. I ran 100m in the same time it took you to run 200m.

You MUST say /in the same time/ when you express that two or more things took an equal length of time to be done, that is, when the time is not a precise moment, but is a duration. They run the marathon in the same time, although their age was quite different; the judges had an hard time we deciding who the winner was.

Generally: at the same time.

Do also others see a face in the waterfall, or is it just my illusion ?

I agree with Jon, but if you mean "simultaneously" then the phrase is "at the same time".