Thymus vulgaris oil is more commonly known as thyme oil. Like most fragrant plant oils, thyme is a source of potent antioxidants but its fragrant components (which are part of the oil itself) pose a risk of sensitivity. For this reason, products with thyme extract are a safer bet in terms of getting the "good" antioxidants from thyme without the volatile fragrance components that, while also being antioxidants, also kick in sensitivity.
Reference for this information:
Cutaneous and Ocular Toxicology, Volume 26, Issue 3, 2007, pages 227-233