Documents with duplicate _id in an index split by time?

Might just be me misunderstanding how ids and indexing work here.

I've got a stream of records and I write them to an index - my_data

Now, to keep it manigable, because there are lots of records, I'm telling logstash to split the index into segments by time:

elasticsearch {
  hosts => ["localhost"]
  document_id => "%{id}"
  index => "my_data-%{+YYYY.MM}" 
}

I then define an index_pattern of my_data-* to drive Kibana.

I've found a case where I initially got the timestamp on a record wrong and when I re-indexed it with the correct timestamp, instead of it replacing the old version with the same ID (the timestamp isn't in the id), it simply created a second copy in the index segment that corresponded to the new timestamp.

Is there anything I have to do to get the id to be unique across all of the index segments? I really need it to be unique within the index pattern...

Document ids are unique within a single index only. You can not make them unique across multiple indices linked by an index pattern.