My DSi is updated to firmware 1.3E. I have rec'd an R4i and confirm it works 100% perfectly in the DSi.
Go on the R4i website and you will see for yourself that the card is supported with updates.
@K3Nv2 I got some cheapies at wallys, that are pretty good, already have lost a few expensive ones (one falls out and gone, can't find) while cutting grass so bought some cheap ones, and of course never lose these cheap ones. (Cheap meaning only $35, compared to air buds which I only have 1 of 2 now)