"Just" vs "already": which one is sooner?

"Just" implies that it happened immediately before you spoke. "Already" refers to some unspecific time in the past.

Just

put the emphasis on when you did (in the very near past)

Already

put the emphasis on the fact that you actually did. It could mean "No need to worry about it, I already did it", or it could mean "you are late, I already did it." for example

When one say:

I've just called him

It means it was done at the moment immediately before saying it. On the other hand:

I've already called him

only implies that it was done before, without being specific as when exactly it was done.