YOU SAID:

the when i did the thing is the time i did that

INTO JAPANESE

私が同じことをしたのはその時です

BACK INTO ENGLISH

That's when I did the same thing.

INTO JAPANESE

その時も同じことをした。

BACK INTO ENGLISH

I did the same thing at that time.

INTO JAPANESE

その時も同じことをした。

BACK INTO ENGLISH

I did the same thing at that time.