Quote and unquote are verbal representations of quotation marks, exactly as you suggest in the beginning of your question. In your first example, they take the place of the quotation marks directly:
Alice said Bob quote intervened unquote.
Alice said Bob “intervened”.
In your second example, they indicate that the following (or occasionally preceding) word or phrase is to be understood as though it's a quote:
Alice said Bob quote unquote intervened.
Alice said Bob “intervened”.
When this occurs, the quoted phrase is probably set off intonationally, so you can hear where the boundaries are despite the word order.
Either version can be used with the same meaning, but I think the latter version is especially associated with so-called “scare quotes”. As Wikipedia says:
When referred to as “scare quotes”, the quotation marks are suggested to imply skepticism of or disagreement with the quoted terminology.
To my ear, this is especially likely when quote unquote precede the “quoted” phrase. It's a verbal signal of irony.