I have have been confused several times (imagine that), as the regin effect of items do not appear in the stats (in either the stat screen or the inventory screen) while in the tower. However, in some cases outside the tower, the regin does not show in the inventory screen, yet it does update the effect in the stat screen.
I do not have enough of these items to tell an actual diff, if it does regin while donning the items and therefore, just a display bug. (like HH suggests) This could be easily tested by someone having enough of the bugged items on, and see if the regin is actually implemented.
