This is the RAW :
A free action with a trigger falls in the category "Other Triggered effects" : it isn't an immediate action nor an opportunity attack (which both occur during someone else's turn).
In the rules compendium :
If an effect has a trigger but is neither an immediate action nor an opportunity action, assume that it behaves like an immediate reaction, waiting for its trigger to completely resolve. However, ignore this guideline when the effect has to interrupt its trigger to function. For instance, if a triggered power allows an adventurer to use a free action to reroll an attack roll, with the hope of turning a miss into a hit, the power must interrupt the trigger ("You miss with an attack") to function: otherwise the attack would be resolved as a miss.
Source : p. 195 & 196 of the Rules Compendium (emphasis mine).
As we're not in the case of "has to interrupt its trigger to function", the free action resolves after its trigger.
In short : your DM is right.