This is definitely NOT what's supposed to happen.
I can vouch for this, since I've also got the Japanese retail CD-ROM boxed release. The proper behavior is for a red slime's explosion to have a limited AOE. When the player character and other enemies are outside the AOE they shouldn't take damage.
Unfortunately in the XSEED version, a dying red slime nukes the entire room. Pretty much all destructible objects in the room are trashed instantly, you cannot avoid damage, and all enemies in the whole room take a guaranteed hit as well even if they're not near the killed slime.
This is indeed a bug. :( I'm hoping it gets fixed.