Mobile app with tabs a bad idea?

I am trying to draw out what I want to build for a new mobile app, and I've run into a conundrum with tabs. I have four main categories of content, and thought it would be nice to have tabs at the top users could select to get to the content they wanted quickly, as shown below. (Please excuse the crudity of my MSPaint drawing. Currently, the Users tab is selected.)

The problem I've run into is in my flow diagram (this is what I'm calling a diagram that shows how one page flows to the next, looked at from a user perspective). Let's say I have content on the Users tab, and I want to add a screen that allows me to add a New User or a screen that that allows me to update an existing user's information. I had thought I would just do a pop up if they clicked on an existing users's name (or New User), but I'm starting to wonder if tabs and popups don't mix well.

Until some of the feedback below, I had thought I did not want to have different breadcrumbs for each tab, as I think that could be terribly hard to navigate (but now I'm re-thinking that). So the root of my question is: what is a common guideline for having more than one screen per tab? Or should I abandon tabs entirely? Each of these 4 tabs could have more than one screen.