The forecast for a TEMPO between 0200-0400 means they are predicting that all weather associated with the TEMPO will be finished by 0400.
It ain't necessarily so.
If the TTF was issued at 0100, thus valid from 0100-0400, it is quite conceivable that the TEMPO appears to expire at 0400 simply because that's when the TTF validity expires. Only a subsequent TTF will make this apparent.