How does this occur doing Tai Chi? 

Vasodilation is experienced when one releases the tension held by the upper body. This done by adhering to principles of Taiji Quan. Such as, keeping the crown of the headed suspended from above, as if pulled by a string. The raising and slight rounding of the upper back, simultaneously with the dropping of the sternum a few millimetres down. The coccyx is tucked in, the knees relaxed and bent. As if you about to sit. All the joints, sinews and connective tissues relax. 

All the tension on the upper body can flow down to the feet and to the ground, the sinking. With the mind connected to the dan tian, a point a few centimetres below the navel. From here, your mind then connects to yong quan (the bubbling well) a point in both feet. Meaning the weight distribution both in the heel and ball of the foot are equal. 

The sinews open. And people usually feel discomfort as the blood vessels begin to open. When they refer to strong legs in traditional Chinese martial arts this what they refer to. Flexible sinews, so the discomfort would be during the expansion (this the eating bitter part for beginners). Afterwards after a pump from the expansion, one may feel the legs are tired. 

So, when the slow form is done properly, vasodilation occurs. People would have big thighs for example however, as my teacher says after two years they go back to normal. As the sinews are opened. But the goal is not having big leg muscles, no. The goal is relaxation, allowing the mind to settle.  

This a light explanation, and introduction, as I am still learning with practice. However, it explains the biology of one of the reasons Taiji Quan and traditional Chinese martial arts have health benefits. And the slow “relaxed movements” that do not adhere to these principles is not tai chi. But an empty shell of movements.