siva krishna jampani as far as I understand your request/idea, this is more a feature request than a bug. I changed the issue type to reflect this. Please clarify if I'm missing your point. Thanks!
As per description you provided for plugin its extension of "Build periodically" Jenkins feature. There its allowing time zone and scheduling time. But in parenthesized scheduler plugin its not allowing. So i raised it as defect.
If it is new feature when it is available to users? it could be better if you done it as soon as possible and its really help full for me.