Buckpuck control with digipot
The first thing to do is make sure your digipots are communicating and switching correctly. Get out a mulit meter and put it across the W and B terminals and see if you see a change in resistance. If you don't then you have a pot issue (or the transistor is turning on unintentionally and shorting out the resistance of the rheostat). Another possibility is the CTRL pin on the buckpuck is shorting things out (you never know).
Test each part of the system separately, find a potentiometer and connect it to the buck puck without the transistor or rheostat connected (or grab an extra one of the bench) to make sure you have the right buckpuck, only the E and I versions have a 5V regulator, if it doesn't have this the rheostat or transistor won't work and you will need to provide a 'pull up' voltage for the ctrl pin.
I'll place my bets that you don't have the right buckpuck, if I read the datasheet right, only the 3021-D-I-xxxx will work in your application.

Edit:
By the way, if you have a 50k or 100kΩ part, you could exceed the current rating as the buckpuck can source 5mA and the 50k and 100k parts can only tolerate 5mA so if the resistance goes low enough you could burn the digipot out the lowest resistance is 45 ohms which is over 100mA which will burn the part out.
From the datasheet of the AD5204:

For example, when VA = 0 V and Terminal B is tied to Wiper W, the
output resistance values outlined in Table 8 are set for the RDAC
latch codes.


This also means that If you have terminal A connected to W the resistance will be backwards (the table is for B to wiper W, so the \$ R_{WB}\$ values will be reversed from \$ R_{WA}\$
So when your design powers up, you default to 84Ω or 45Ω (depending on your part) and more than likely burn up the AD5204. You need to have series resistance to protect the AD5204
From the Absolute maximum ratings section: