はやる "hayaru" and 人気 "ninki" are two different words that are both translated as "popular" in English. However, they are not exactly the same.
はやる is something that refers to a fad. For example, a hairstyle, a genre of music, or a style of clothing can all be described by はやる. The progressive form はやっている is often used because something in fashion is considered to be in the here and now, so there is a limited time scale involved -- something that is はｙっている now will not be はやっている in the future. When talking about something that was popular in the past, the past progressive form はやっていた is often used.
Bitoruzu no ongaku wa rokujuunendai ni zuibun hayatte ita.
The Beatles' music was very popular in the 60s (and it wasn't anymore by the 80s).
Konogoro Nihon dewa donna heasutairu ga hayatte imasu ka?
These days, what kind of hairstyles are fashionable in Japan?
人気, on the other hand, is used to refer to a person or thing who is known by a lot of people. Note that it does not have the connotation of being in fashion or being the fad, i.e., there is no limited time scale required. When something or someone is popular, you say 人気がある. When someone or something becomes popular, you say 人気が出る。
Bitoruzu no ongaku wa rokujuunendai ni zuibun ninki ga atta.
The Beatles' music was very popular in the 60s. (a lot of people liked the Beatles then).
Soccer is popular (well-liked by a lot of people).
Nihon de sakkaa no ninki ga deta no wa suunenmae datta to omou.
I think that soccer became popular in Japan many years ago.
Miura, Akira. Essential Japanese Vocabulary, Tuttle.