Venture Coffer and Retainer gear reward level (possible bug)

[LibitIncarne]

This is off/extra topic question: will higher ilvl increase the chance I'll get that bonus tier reward in a general?

Wasn't able to respond earlier because of the 50/day limit.
Higher IL increases the chance that you'll get the bonus tier reward, but only in that you'll be more likely to have something that your IL is high enough to have the bonus apply to.
Housing Items and Dungeon/Tome gear can never have the bonus tier applied to it, and the 1 crystal fallback can't either.