Let's divide the verse into two parts:
נשאו נהרות ה'—נשאו נהרות קולם
and
ישאו נהרות דכים
Each part is one sentence.
The first one is broken up poetically by a caesura, around which both the subject and verb are repeated. So the reason "נשאו" and "נהרות" are identical in each of their appearances is simply that they are repetitions of the same word.1 And the invocation of God's name is an apostrophe, so let's move that to the end to simplify things. Then we are left, more or less, with
Floods have raised their voices, God
This is an observation of an event or series of events that has happened, so the verb is perfective. Without getting bogged down in the spectrum of tenses, it is pretty expectable for it to be translated in a past continuous or present continuous tense for that reason.
The floods lift up their fall2
This is a prediction or a promise, so the verb is imperfective and it is rendered in a future or present tense in translation.
Rav Hirsch explains in his commentary (p. 162) that the noisy rushing waters stand for powerful nations who have continually raised their voices against God (past), but, as is the case with mighty waterfalls, "the 'lifting up' of the nations' voices is only a prelude to their decline" (future).
You may notice that I listed some form of present tense for both verbs above. This might be confusing in a vacuum, so hopefully the meaningful difference between observation and prediction clarify the difference in the original. English's present tense can include both perfectives and imperfectives, which may be the sticking point in the imbalance of translations.
1Kind of like, though not exactly, the word "tapping" in "And so faintly you came tapping, tapping at my chamber door" (Poe). Semantically it is only there once, i.e. it could be read "you came tapping at my chamber door" without changing the meaning.
2This is the translation of Rav Hirsch.
