No they are not forest dwellers. They lives on theplains.
From the internet
Tigers are carnivores, and their diet in the rainforest consists of monkeys, wild oxen, boars, antelopes, birds and other animals. While they often attack herbivorous animals, tigers prefer killing young, weak or old animals because they cannot run as fast and are often left alone by their herd.
Bengal tigers live in the tropical rainforests of India, Bhutan, China, Indonesia and Bangladesh, though most of the population is found in deciduous forests and grasslands. One of the largest in its kind, the Bengal tiger has black stripes and a coat that is darker than that of other tigers. When combined with the shade of the trees, their striped coats allow them to blend with the forest floor. They have soft padded paws and retractable claws, making it easier for them to stealthily and quickly sneak up and attack prey. Bengal tigers have nocturnal vision, which they inherited from their saber-toothed tiger ancestors. Their excellent night vision allows them to hunt for food throughout the day and night.