Put a period at the end of the sentence so Google (and everybody else) knows the sentence is complete.
You will find it translates back and forth faithfully.
The problem is that the OP is using 必要 as though it were a noun, when, as far as I know, it's more frequently used as an adjective. That said, there is some
eccentricity on the part of Google, as well (of course).
Google translate does this:
必要 - "need"
私は - "I [subject marker]"
私は必要 - "I do not need"
So, unless there's some expression in Japanese with which I'm unfamiliar (which is entirely possible, since I'm not that skilled at the language), the OP is correct in pointing out the interesting confusion.
That said, we are not making the clearest sentence possible. One solution would be to make the statement a bit more specific - say, for example:
Since we're now using 必要 as an adjective, everything's fine - at least from Google's perspective. We're trying to say, "Me leaving in 15 minutes is an important thing," instead of "Me leaving in 15 minutes is a necessity," which, at least in Japanese, I believe makes more sense.
But then there's this ておく business which, frankly, complicates the sentence. The sentence actually says, "Me leaving 15 minutes beforehand important thing," which doesn't make any sense, since the subject of the sentence isn't really "me," it's "me leaving 15 minutes beforehand."
TL;DR - You can't use English grammar and syntax when speaking Japanese; Google can be strange, but that sentence isn't really a very good Japanese sentence from what I can tell. I explained the original issue, and now I'm not touching it anymore. :P