The documentation is a little misleading when it states: "The rule does not run when a record that previously met rule criteria is updated". Makes it sound like a record can't qualify again.
So for updated to work, the record needs to be updated from something different than the entry criteria condition, to something that equals the condition.
For example, entry criteria is "some_number_field > 0". If the value is 1 for first entry and you change to 2, it wont trigger and re-enter. You would need to change that value to 0 to disqualify and then to 2 (or anything greater than 0) in order to qualify.
To get around this I created a new custom field as a boolean on the object. Journey entry criteria is then set to "New_Field = False". When I create the new object I set the field to "False" which enters the record into the journey. Then in the first step in the journey I set the New_Field value to "True". When I want the record triggered into the journey again I set to "False" again.