s5 has three successors in the structure: s0, s2 and s4 (which you also see in the tree).
The "<>" operator talks about the existential predecessors, so node 12 in the tree argues about:
"Tree-Node 12 holds if there exists a node satisfying x2 of which s5 is a predecessor"
As the node s2 satisfies x2 (as a & !b holds there), this condition is fulfilled; so regardless of what happens with the nodes s0 and s4, tree-node 12 does hold due to tree-node 20. In local model checking, the "<>" operator acts as a disjunction, so if one of the tree-nodes below satisfies the property, the node with the "<>" is also satisfied.
In contrast to that "" acts as a conjunction, so in this case if one of tree-nodes below does not satisfy the property then the node with "" also does not hold.