Curious. I don't know what effects Twilight menu and the rest have on things here, and with it and flash carts being as prevalent as they are then I can't imagine download play gets tested that often. Local (as in between cartridges) is an interesting too from a historical perspective as very little has troubled that.
Outside of it being an issue with the hacks/software itself (such things are not the most accurate, hence the need for anti piracy patches originally externally but today increasingly integrated) it was noted many years ago that trimming ROMs in various manners troubled download play. Indeed grab some old trimmers and they might note themselves as being download play safe (forget the definition went with but something like the value of the size in the header plus a few hundred bytes). If you have trimmed a ROM (does it come as a power of 2 size, that is to say 16 megabytes, 32, 64, 128,256, 512...) then for the sake of testing go back to untrimmed ones. I don't know what the various dumpers do here as far as trimming things for you (possible some would consider it redundant data and not bother) but it is the main thing I know of in this.