Assuming that with posters you mean the manga cover images and/or anime cover images. Then no, they do not have to pay for displaying these.
Often these images either fall under the Fair use of thumbnails on the internet
Use thumbnail images (150 pixels). These small images are generally considered fair game for artwork and photography, so a book cover in this size should be legal under copyright law based on precedence set in court cases.
And in cases where they are bigger than 150 pixels, they often still fall within fair use policies for myanimelist and animeplanet .
In its most general sense, a fair use is any copying of copyrighted material done for a limited and “transformative” purpose, such as to comment upon, criticize, or parody a copyrighted work. Such uses can be done without permission from the copyright owner.