Ring MTX Displays on Opposite Hand

So I have the Ring of the Demon Slayer MTX, and it displays on the opposite hand on my character from where I place it in the cosmetics window.

If I equip it on the ring on the same side of the cosmetics window as my shield, it's visually on my character's weapon hand, and if I equip it on the same side as my weapon, it's on my character's shield hand.

Does it always display in off hand? Or does it switch hands when you change slots?

Also, you're playing a templar. He's a lefty so his weapon hands are switched, but it's possible that doesn't apply to rings because they normally don't have visuals. (as in, GGG forgot or decided not to do that)

Edit: I've tested with Lori's Lantern, and as I thought, main hand side slot appears on right hand and vice versa, like on all characters. Basically, templar's hand switch only applies to weapons, which makes sense, but might look confusing at times.