Is there a psychology term for an adult that has tantrums?

Depends: This sounds like a problem with emotional regulation and impulse control, but the diagnosis would be determined by the nature of the tantrums and other emotion & behavior factors. For example, if the tantrums are aggressive/violent, there could be an Intermittent Explosive Disorder. If they're emotional outbursts, it could be related to a mood disorder.

Not exactly, but...: An adult who has a histrionic personality disorder might be more prone to throwing "tantrums." People with HPD tend to have a psychological (and largely unconscious) need to be the center of attention. They are often very theatrical in their behavior and demeanor.

Symptom : Tantrums are a symptom. Are there other symptoms?

Not offically: There are people of all ages that experience what some of us would see as Tantrum behavior. When you break it down, age 3 or 53 it is emotional dis regulation with inability to control your thoughts, feelings and behaviors until it just consumes you. It is typically learned to control in early childhood but not all of us benefit from that knowledge for multiple reasons.

Anger management : Low frustration tolerance and explosive angry outbursts. Cause needs to be determined.