The lifespan of T cells varies from months to years (memory T cells). T cell development begins in the bone marrow and continues in the lymphatic tissue and periphery. During their lifespan, these cells circulate in the body and migrate based on chemical gradients.
What happens when you exercise? Blood pressure increases, blood vessels dilate. I honestly would not be surprised if what these authors observed was just existing T cells in capillary beds being kicked up into circulation, only to adhere and begin to intravasate a couple minutes later.