とみると follows a plain-form clause and means "on judging that", "seeing that": someone sizes up a situation and acts on it straight away. A noun or な-adjective keeps before it, and the second half is the action they took.
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As soon as he realized he couldn't win, he ran away.
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Seeing that the enemy was weak, they launched an all-out attack.
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As soon as the children saw the teacher wasn't there, they started making noise.
The clause before とみると is a judgment, not only something seen: and are conclusions. The person who judges is usually the one who acts, and the action often has a calculating edge – taking a chance, cutting losses.
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As soon as the president saw there would be no profit, he cancelled the project.
とみると or と見るや
says the same with more urgency: the reaction comes the instant the judgment is made. Both belong to writing, news and narrative, and と見るや is the more literary of the two. In conversation,
or
does the job.
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The instant he saw his opponent drop his guard, he struck back.
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Once he found out his opponent was weak, he suddenly got cocky.
とみると or たとたん
is pure timing: one thing happens and the next follows at once, with no one judging anything. とみると needs someone to weigh the situation.
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The moment I opened the door, the cat shot out.
Lingaku