Usage of already, yet, just etc.

[DevDev]

It is correct to use these words in Present perfect tense like

I have already completed it

He has not arrived yet

I have just come in

But, at times, I notice people are using this with Past tense as well.

Like, he just left, etc.

Is it correct, please give more details, thank you.

[Matian]

you are damn right,
but you need to know just has a different meaning,so that other usages and in first example it means "only a short time ago"
like"I've just been shopping"
but in a second one it means"at this moment or at that moment"
like "he was just leaving when the phone rang"

[Josef]

But, at times, I notice people are using this with Past tense as well.

Like, he just left, etc.

Is it correct, please give more details, thank you.

I believe that is normal usage in American English, in the same way that AmE often uses the past simple instead of the present perfect. It is less common in British English.