Can't sync Excel to OneDrive without closing it after saving

Sounds like your using older OneDrive for Business sync client on the other computer and it's opening the file locally instead of on the cloud so the file stays open, and saves, but until you close and the file is unlocked the sync client then sync's the changes up.

It could also be an older version of excel you they are opening the document up on as well that doesn't understand onedrive files being opened locally need to open from cloud directly instead of local.

Can you get the version of the sync client and version of office as well? I know some office sku's cannot edit online as well if memory serves correct.