What Does Ophthalmologically Tested Mean?

This claim means that a product has passed the eye area tolerance test and thus the packaging can say "ophthalmologically tested".

Does dermatologist tested mean tested on animals?

Nothing. “Dermatologist tested” is one of those terms (like hypoallergenic) that is not regulated in any way. Of course, if you want to print “dermatologist tested” on the packaging, you need a dermatologist to test your product.

What does dermatologist cruelty free mean?

The term cruelty-free typically means that a product has not been directly tested on animals; therefore, there is no animal cruelty involved in the finished product.