Is this a case that I need to just ring ahead and ask that they prepare my double room as a twin, or is this too presumptuous?
I usually use booking.com for my hotel searches, and they've previously let me select twin rooms, if that helps at all. I suspect it's largely dependent on the search tool itself.
Terms vary country to country, so it's always a good idea to make sure you confirm that what you're getting is what you're after.
In the US a "twin" bed refers to a the same thing that a "Single" bed refers to in most of the rest of the world. ie, one bed, suitable for sleeping one person. If you're after a room with 2 beds it would normally be stated as explicitly having 2 beds - something like "2 twin" or "2 Queens".
For non-US, "twin" in a hotel/motel would normally refer to 2 beds, which could be two single beds, or two larger beds (double, aka "full" in the US, or queen). eg, you might find a "Twin Queen", a "Twin Single", or even a "Twin Queen/Single" which would have one or each.