Are you using filters or triggers? If using triggers, then if someone either receives email 1 or clicks on any link, then they will transition to the second stream.
You can run a smart campaign to manually change people's stream using the Change Engagement Program Stream flow step
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Provide some screenshots.
And avoid using transition rules. They are limited and more difficult to debug. Batch smart campaigns are much better. No need for triggers, since EP casts are on fixed timeframes.