The U.S. pronounciation of the word "dig" puts the "i" vowel nearer to "e". In the Weat african, Senegalese Wolof, the same word means to "hear/understand" or "get it" ( get the jist of). This useage of this word in the "anglophone" world seems to have emerged in the 1960s with the rise of "black" (African) Americans and the acceptance and explosion of Afro based music, ie, soul, blues, jazz etc. I hope this contribution is helpful as I have been a little frustrated in finding any references to African language migration within English language dictionaries.
I am a half Irish, "white" born in UK, and have travelled quite considerably as a musician, and as a fluent "wolof speaker have got to know several words whos migration has enhanced the "English language.