Yes, it is synonymous to "только что", but it does not matter whether the past or present, imperfective or perfective is present. As far as I can remember right now, it means a very close position, juxtaposition, coincidence of almost anything (subjects, actions, sizes, you name it) — literally and figuratively.
Here the talk with someone's daughter ended right before these words were said/written, so they, the conversation and the words almost coincided:
Я как раз разговаривал с твое́й дочкой.
I was just having a talk with your daughter.
Here the talk with someone's daughter is going exactly at the moment when these words were said/written, so they, the conversation and the words coincided in time:
Я как раз разговариваю с твое́й дочкой.
I am just having a talk with your daughter.
Here the size of the shoes and the size of the speaker's feet coincided:
Эти ботинки как раз мне подходят.
These shoes are exactly/right for me.
Here the fact or forecast of a rain coincided with implied weather opposite to the shiny weather:
Будет ли солнце? Как раз наоборот, будет дождь.
Will it be shiny? Exactly the opposite, it will be raining.
I think, it's important to note, that как раз in some situations can be used with some words in a sentence omitted, but I'm not sure whether such cases are not part of a broader issue in speech, not related directly to "как раз". In such situations the omitted/implied part of a sentence should be clear from the context:
Here the word "подходят" has to be inferred:
Как ботинки? Как раз [подходят]
How are the shoes? They fit fine.
Here the word "наоборот" has to be inferred:
Будет ли солнце? Как раз [наоборот] будет дождь.
Will it be shiny? Quite the opposite, it will be raining.
John: Это далеко; It is far away
Kate: (Нет,) как раз близко; (No,) right the opposite, it is near