The easiest way right now is by using
Information[p, "DecisionTree"] // Head
(* Tree *)
However, keep in mind that this tree is not acting on the input data but on the processed data.
You can force the processing pipeline to be minimal using
Predict[data, Method -> "DecisionTree", FeatureExtractor -> "Minimal"]
which in this case is removing the standardization.
With non-numerical data you will still get a tree that works on something else though.