Right now, characters who have the same planar race can recognize each other immediately, or this appears to be the case. I have played a few planars recently, and all of them could spot others of their kind staight out of the boat. This applies even if their base races are different. Example:
Tiefling spots apparent halfling, but can then see it is in fact a tiefling. Same applies on aasimar/genasi.
Planar characters are varied, and not two of them is the same. There is no reason aasimars would know the other person is aasimar, same for specific genasi bloodlines, and tieflings. Heritages vary so vastly, and tieflings/genasi/aasimar may not know of their own heritage either.
There is mystique to the planar bloodlines, or should be. Add lore check to recognize your own planar types, as it is with everything else. Even Elves cannot tell other elves' subraces without lore investment.