Neo4j does not mutate data, or do anything you don't tell it to do.
Neo4j does support many kinds of instant (date, time, datetime), and duration datatypes for recording time.
There are many ways to set modification times on nodes and edges, such as with triggers, but best would be to plan for it before designing your graph model, and simple include the Cypher in any parts of your code which modifiy the data:
MERGE (n:Node {id: $someId})
// do stuff
SET n.date_modified = datetime()
