The concept of a continuous transform is to continually increment and process checkpoints as new source data is ingested. The timestamp used for synchronizing source and dest must follow real time, meaning it must be a recent timestamp. To adjust for index delays, e.g. because the timestamp you use runs behind due to processing delays, you can use the delay parameter, default 60s. That causes transform to deduct the delay when querying data, e.g. lt now-delay.
If you process historic data, there is no need to use a continuous transform, but you can use a batch transform. Is there a reason you want to process historic data but still use continuous mode?
There is a trick, instead of using the historic timestamp, you can add an ingest timestamp while you are feeding in new data, here is how. You than use the ingest timestamp for sync, you can keep your timestamp_max and timestamp_min as is.