How to interpret the execution of distributed computation from time-space diagram?
Yes, it is ambiguous, and it is ok. A single space-time diagram can be linearized (collapsed into a compatible sequence of configurations and events) in many ways, potentially an exponential number of ways. E.g. imagine that you have 1000 nodes, and each of them performs a local operation. Obviously there's 1000! different ways to linearize this, because there are no inherent causality constraints in this situation.

It is not true that events in an execution are totally ordered. They are only partially ordered, using the partial order given by causality constraints (most of which are "a message is sent BEFORE it is received"). There are many total orders compatible with this partial order.