Asphalt based products are the mainstay of the roof repair process. Thave been around forever, are cheap and people are comfortable. Unfortunately, they don't last very long and are a real mess to use and clean up. Contractors make them work but homeowners have more trouble.
Fibered aluminum roofing compound is a product with aluminum mixed in with the asphalt. When well mixed and applied to a clean, dry roof it sticks well and creates a shiny surface that reflects light.
You can buy rolls of fiberglass mesh to embed in the asphalt. The technique is to put down a layer of compound, lay the mesh over it, force the mesh into the compound with a trowl, and then put another layer of compound over the top. With the mesh added, this will allow you to cover gaps and make a longer lasting repair than you get without the mesh.
Cleanup is the pits. I always got tar on my hands and clothes, not to mention the tools. Cleanup is with gasoline. That is both dangerous and hard on your skin.Rubber gloves would help but there is no avoiding some mess.
After you have repeated this repair a few times you start thinking there must be a better way. On your next trip to the home improvement store you will be attracted to the elastomeric coatings.