I heard many people saying "he just left the room", but I read that just(recently) is used with present perfect. So are people just omitting has?
He just left the room.
He has just left the room.
Both the sentences are grammatical, without any difference in meaning.
The adverb just means very recently. In BrE, the usage of the present perfect for recent actions is dominant, whereas in AmE, the past simple and the present perfect are equally used.
You may say either.
He just left the room / He has just left the room.
She just ironed that shirt. / She has just ironed that shirt.
There is no real difference between these two forms. I expect there are some people who prefer one over the other, but both are natural English.