They were able to easily make the holes because those statues were hollow.

In the only technique for doing large castings, the Lost Wax process, a statue would be sculpted in clay, a mould ( a mix of plaster with clay) of several pieces would be made around that statue and pulled off, beeswax would be applied to the inside of the mould until a thick later was built up, then more clay would be used to cover the outside of the mould to make it stronger, and more clay used to fill the inside of the statue. Bronze pins would be driven through the whole assembly, to help hold it all together. Then it would be baked, so the wax would run out/ be burned off. Molten brass or bronze would then be poured into the mould, to take the place of the wax. Then the shell was knocked off the outside, and the clay core removed from the inside.

That's an extremely concise, basic description. As you can imagine, making it all work nicely to produce a pretty statue at the end was much more complex. But drilling a hole into the mouth of the statue was therefore comparatively easy, and rolling up and soldering a copper tube to run up to it from the base of the statue not very difficult.

You can search under "lost wax casting" and find any one of a number of useful diagrams online, but here's one that's pretty clear.

Now, providing water under pressure to constantly go though the fountain was another challenge. If there wasn't a source of water that could simply be made to run downhill, there were not many good options in the period. . When Louis XIV wanted to have lots of fountains at Versailles it was necessary to build a huge number of pumps and watermills to power them. You can read about that here.