I've read some said it's needed and some said it doesn't. Is there any experienced stringer here that can clarify this?
Actually, you'd need extra tension on the mains EVEN IF your head was square ...assuming you string the mains first. The extra tension (I've actually calculated this as +1.4lb for a symetrically tensioned ISO head with diameter 0.7mm nylon string) is needed because the crosses (strung second) deform the run of the mains (strung first), increasing the length a mains string has to run and therefore increase the mains tension.