Is this a double negative?

This sentence seems like a double negative to me...

okane o zenzen motte imasen

I thought zenzen means "none" or "not at all" and that motte imasen means "not in my possession" or "I don't have". So to me it sounds like "I don't have none" which mean that I have "some". Am I understanding what zenzen means? I got this example from here...
Pimsleur Japanese 1 Lesson 11-15 flashcards | Quizlet

I understand that zenzen can be translated to 'at all' or 'totally'.

お金を全然持っていません。I don't have any money at all.
全然知らない！I don't know at all!
全然いいですよ。It's totally fine, you know.

So I'm pretty sure that's not a double negative.

Yeah, it's just a simple negative. As in the note "use only in negative sentences" in your linked page, "zenzen" means "not at all" in negative sentences or with negative expressions like "zenzen dame".

全然 + ない is part of a series of pairings where a word at the beginning of a sentence is paired with a specific verb conjugation or phrase at the end of the sentence. My professor told me the linguistic term for this but unfortunately I can't remember it at the moment. He also told me that one of the theories as to why Japanese does this is that in long sentences, you're sort of giving the listener an idea of what is coming at the end (the verb tense).

Another example of a pairing that seems a bit redundant:
危なく + [verb]ところでした : almost did [verb]
In this usage, 危なく means "almost did" rather than "dangerously" (which was my first instinct), and [verb]ところでした also means "almost did". Though perhaps the 危なく implies that the activity that was almost done is undesirable?

I'm sure I know more of these pairings, but I can't think of them at the moment. If anyone can remind me of that linguistic term I mentioned, I would appreciate it; I think it is [something]ぶし, むし, or some u-sound + し? I'm not sure haha.