The marginal shift probability tree is a copy of the target phylogeny, but where each branch length is equal to the branch-specific marginal probability that a rate-shift occurred on the focal branch. For example, a branch length of 0.333 implies that 1/3 of all samples from the posterior had a rate shift on the focal branch. Note: It is highly inaccurate to use marginal shift probabilities as a measure of whether diversification rate heterogeneity occurs within a given dataset. Consider the following example. Suppose you have a tree with topology (A, (B, C)). You find a marginal shift probability of 0.5 on the branch leading to clade C, and also a marginal shift probability of 0.5 on the branch leading to clade BC. Even though the marginal shift probabilities appear low, it may be the case that the joint probability of a shift occurring on either the branch leading to C or BC is 1.0. Hence, you could be extremely confident (posterior probabilities approaching 1.0) in rate heterogeneity, yet find that no single branch has a particularly high marginal shift probability. In fact, this is exactly what we expect in most real datasets, because there is rarely enough signal to strongly support the occurrence of a shift on any particular branch.
The cumulative shift probability tree is a copy of the target phylogeny but where branch lengths are equal to the cumulative probability that a rate shift occurred somewhere on the path between the root and the focal branch. A branch length equal to 0.0 implies that the branch in question has evolutionary rate dynamics that are shared with the evolutionary process starting at the root of the tree. A branch length of 1.0 implies that, with posterior probability 1.0, the rate dynamics on a branch are decoupled from the "root process".