Now that I think about it, has they referred to grandpa Hino as Hino in the manga? I have a feeling this is to do with the old show and even then I am not sure wether they ever said Grandpa Hino. Needs to be checked. I think he has always been refered to as Rei's grandfather, so it might be entierly on the fanbase and wrong translation.
But yeah, it's most probably meant to be her paternal grandpa, even tho it's not explicitly stated so.