Did John Tyler pursue Manifest Destiny?

Yes, John Tyler, like many presidents before him, pursued Manifest Destiny policies in order to justify Westward expansion of the United States.
Tyler's main contribution to this expansion was the annexation of Texas. Texas had previously won its independence from Mexico and had sought to join the States. Prior presidents had been wary of allowing this because it might force a war with Mexico. There were also concerns that the public would not support annexation of Texas because it would be portrayed as an attempt to increase the reach of slavery and the political power of the slave states. John Tyler was aware of these concerns as well, but he was determined to annex Texas and helped obtain the necessary agreements to allow Texas to become a state.