As you probably know, plywood essentially won't move at all since the individual plys have grain oriented opposite each other, so the long grain in one ply locks the crossgrain in the other.
Assuming we're talking white oak here, you can guess at movement with a calculator: http://www.woodweb.com/cgi-bin/calcu...ator=shrinkage
In this case, assuming typical seasonal fluctuation of 4 to 14% moisture content in the wood, which should be slowed down once you finish the wood, and it's flat sawn, your 1" rails will move about 1/32" The 3" panels could be more like 1/8". And again, this is a worst-case scenario, since if you put a coat of poly on, it will slow down the wood's rate of absorption of humidity quite a bit.
Either way, you shouldn't have to worry. If you dado the rails and glue them to the plywood tongue-and-groove style like you mentioned, the plywood itself is going to hold the inside of the rails pretty tightly. The rails may expand towards the outside a tiny bit, but not nearly enough to cause problems here.
The 3" oak border, depending on how it's secured to the table, is probably even better off. Even if it moves a little bit more, it'll simply push away from where it's secured to the table (towards the outside) as it expands. No problems.
In general, I've discovered the rule of thumb is to not worry much about aprons, legs, rails, and other narrow pieces moving. Once they're glued up with good strong joints and finished with whatever you're putting on, they don't seem to go anywhere. If those panels were solid wood rather than plywood, you'd probably have to allow room for expansion in the 1" rails, but as it sits, you're good to go.
I thought Matthias Wandel's explanation of moisture content and wood movement was really helpful: https://woodgears.ca/lumber/moisture.html