Not able to interpret decision tree when using class_weights
We should consider two points. First, class_weight='balanced' does not change the actual number of samples in a class, only the weight of class $w_{c_i}$ is changed. Second, the [un-normalized] probability of class $c_i$ in each node is calculated as

$w_{c_i}$ x (number of samples from $c_i$ in that node / size of $c_i$)

For example, in balanced mode, the [un-normalized] probability of $c_3$ in the green leaf is calculated as

$33.\bar{3}\% \times (3 / 36) ≈ 2.778\%$

compared to $36\% \times (3 / 36) = 3\%$ in unbalanced mode.

The probability (normalized) in balanced mode would be: 

$100 \times 2.778/(2.778+32.258) \% = 7.9289\%$

Remark. The word "probability" is not applicable to each isolated node  except for the root node. This is the un-normalized version of the probability used to classify a data point inside a leaf, though the normalization is not required for comparison. However, the notion is applicable to the aggregate of nodes at the same level and the leaves from upper levels (i.e. set of all samples).