In Italian, when you fill something with a liquid (or powder), you use riempire di.
Examples:
• Riempire un bicchiere d’acqua (“fill a glass with water”)
• Riempire la vasca di schiuma (“fill the tub with foam”)
You could use con to talk about filling a container with distinct objects (e.g. libri, fiori), but liquids normally take di.
Here a + la = alla marks the place where you’re performing the action: “at the fountain.” You’re going to the fountain and filling the bottle there.
• If you said dalla fontanella, that would literally mean “from the fountain,” focusing on the origin of the water.
• Nella fontanella would mean “inside the fountain,” which doesn’t make sense for filling a bottle.