It should happen immediately. Does The Who work and sort into T? If that works (and I think it should because someone else did this before and reported it working), then maybe there is an issue with Numbers and The.
EDIT: Apparently it does not, I just tried. Oh god. I was sure that it does and someone confirmed it in the past, so didn’t check again 
But I found that there is a workaround: Omit the spaces in the sort order field in the artist editor (I have artist name Sort by Last Name in Settings):
Side note:
The sort name works for me generally and I use it all the time actually, though not with The because I am fine with “Who, The”. So I didn’t recall this no-space requirement from the top of my head. E.g. what works for me:
- Roon does not recognize the German “Die” instead of The, so if an artist is “Die Türen” it gets sorted under D. Then I change the sort order to “Türen, Die”, and this works.
- It also works in cases where there is a band with an artist name and this is not reflected by default in the artist’s sort order info. E.g., Mark Lanegan is sorted into L by default (if sorting is set to Artist Last Name), but Mark Lanegan Band was sorted into M. So I changed that to “Lanegan, Mark Band”, and this works as well.