I believe by "cross-context stability", they mean a behavioural pattern exists across a range of contexts. This establishes it as something deeper and consistent within the creature, rather than something caused by a set circumstances. The thing they were telling you to avoid is having common factors between your objects or scenarios. If there is a common factor other than the one you intend (new object), then you do not know that common factor is not the cause of their behaviour instead. So you need a set of tests that have nothing in common except the thing you want to test for. If you see the same behaviour from the cat in all tests, you have a case for saying that thing determines the cat to behave in a certain way. If you do it for all the cats, you have a comparison between cats, and can look for trends there. The main thing is to have data that is meaningful and you can conclude something from with some certainty.