Yeah, I'm trying to get my head around it too. These contextless sentence fragments really don't help us learn anything.
A word for "with" in this context would be kwa rather than na though. If in doubt, remember that kwa is more like "with" when it means "using", "by use of", and na is when it's "with" as in "together with", "accompanied by".
Here's a bunch of examples of this in use to have a look at: https://glosbe.com/en/sw/fill%20with%20water
From the examples, it looks like you don't use a word for "with" at all.
If something fills with water (on its own) you say i-na-jaa maji. If you fill something with water, you say ni-na-i-jaza maji. So, I guess jaza maji would be "Fill it with water", with the "it" being unspoken.
This means "fill it with water" and the Swahili is correct. All languages are idiomatic and contextual and Swahili is no different. I think we are anglicizing it to add the "na" preposition in there.
If you want to understand this construction consider the common verb-noun combo in Swahili functioning as a type of compound verb, such as kupiga picha, kukata tamaa, kuona huruma
(i.e. kumpigia rafiki yake picha, kuonea watu wao huruma, kumjazia mwanawe maji)
All languages are especially confusing in terms of how verbs interact with prepositions and which verbs are transitive or intransitive.
For example in English the word "to wait" is intransitive and requires the preposition "for". i.e. "I'm waiting for Juma" but in Swahili the verb is transitive and is simply "namngoja Juma" and requires no preposition. Same in French "j'attends Juma"
I keep missing this, because "what does this even mean?" The guy below says, "fill it with water." okay, I guess, but then why does this translation always use the word "up"
I don't think "jaza maji" and "jaza petroli" require "na" or "kwa", and word order may vary, "jaza petroli tangi" or "jaza tangi petroli" (as in "kumpiga mtu picha" and "kumpiga picha mtu"), but the word "tangi" may often be omitted.The translation should be "Fill with water" or "Fill it with water."