How long does it take to someone to master backend web development with either in spring or asp.net?

Depends on the level of mastery. There's still portions of the frameworks I'm not adept at, and I've been using both since inception.

@SortOfTested I am talking with respect to level of mastery of knowing in and out of the server (you know what I am talking about if you worked on iis and asp.net mvc), writing performance effective code, knowing all the annotations, knowing everything about the working of different extensibility options of the framework i.e. package bundle configurations, customized view engines etc.

IMO it's not worth it to know it all inside-out. It's just too big. The moment you finish your Spring checklist your knowledge on the first items in the list will be obsolete.

Just know enough to do your job well. After all, it's just a framework, not a widely-applicable concept. I'd say focus on those instead, as they are framework (and for the most of it - language)-agnostic.

@Prometheus
Those would be the basics to my mind. What @netikras said, and estimate, about a month of practical application should be sufficient for each.