imessage question

We have 2 iphone and 3 ipads. My iphone is new, never had one before. I went to erase my messages using clear all and some how they can be accessed on the ipad/iphone. is it archived or what settings can we use so each imessage is a little more private? if I do the delete are they really deleted or do they go through icloud somewhere? Please advise because I am still learning this phone. Thank you.

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