My usual strategy for that is to write out a summary of the character's thought processes so it's OOCly clear how they're coming to the conclusion they are. Time-consuming but I've never had anyone accuse me of infomodding.
This is what I do for my character who is shown in canon to be able to read most people like books. He does it by picking up on context clues, just like you said.
A lot of people don't remember that characters can read public threads (I definitely forget it all the fucking time) so having a little ooc spiel of how your character realized x thing is very helpful. Otherwise... yeah, I can definitely see how people could jump to the infomodding conclusion.
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