Oh boy, you just opened a can of worms... Refillable mugs are a touchy subject! In my past stays we were told that they were good for future visits to that Resort, but now it seems that you are NOT supposed to use refillable mugs from previous stays, even if it is from the same Resort!
I have emailed Disney on this topic before and the official answer is no.
They do not police it - it is an honor system.
Many on this board feel that if people abuse the system it will ruin it for everyone else. Many others feel that if Disney doesn't police it - what does anyone care.