Does a full tear of the gluteus minimus tendon result in a long-lasting inflammatory response?
The article you linked is interesting, but as @Charles E. Grant mentioned in the comments, it’s not particularly reasonable to compare a non-tear repetitive stress injury (like epicondylitis) to a full muscle tear. Non-tear repetitive stress injuries persist because the offending frequent motion doesn’t stop. A muscle tear, however, will recruit an inflammatory response that will eventually be resolved by anti-inflammatory factors (Th2 cells directing the cellular microenvironment towards healing / scarring). 

This healing process might not result in an optimal resolution of the initial injury, and it’s not unique to any particular body system. Rather, pretty much anything in your body that can be injured will first respond with a period of innate inflammation followed by fibrosis and resolution (whether or not that restores function / alleviates pain depends on a number of factors including injury severity, therapeutic management, and healing conditions e.g. if there were repeated injuries during the healing process). 

With regard to gluteus minimus tears — it depends on the injury. If a patient persistently aggravates an already-torn muscle, they will have more inflammatory cells recruited to the injury. If they do a good job allowing the injury to heal (not re-aggravating the injury, receiving surgery if structural correction is required), the inflammatory process will resolve relatively quickly.