You could contact the city or county to complain, but it's not likely they're going to show up with heavy equipment one day, tear out the offender's new drains and correct the problem. Inevitably, you will have to hammer out a solution with the neighbors. You could go to court to make these folks cease their actions and possibly receive recompense for damage. You would have to prove the neighbors unreasonably altered their property, resulting in surface-water damage to yours. In most states, by the way, you'd have to prove both damage and nuisance. All told, this route could prove costly and not exactly make for glowing neighborly relations with the uphill clan.
First, show some diplomacy and try to work things out with the neighbors. Before doing that, you may still want to contact the city to see if the neighbors have a right to do what they did (doubtful) and then a landscape firm to see what your remedies would be and how much they will cost. You'll at least be forearmed with the "cost" part of the equation before your neighbor meeting.
A landscaper may suggest you install a berm or retaining wall along the property line to stop or deflect the flow or possibly carve out a catch basin or cross-property ditch reinforced by a plastic liner and (or) gravel. The best remedy would depend on the lay of the land. Get some quotes, then, as politely as possible, tell your neighbors any problems you are experiencing and what would need to be done (and spent) to mitigate the issue. Ask if you can work together on a solution such as them redirecting the rain to a more benign route.
Any remedial landscaping costs should be, at least in a perfect world, shouldered by the neighbor; however, feel free to kick in a little out of good faith if you sense that will help. That might sound galling, but it would still be cheaper than court and might prevent future Hatfield-McCoy-esque confrontations and additional things cascading down onto your property.
If the neighbors balk, then consider plan B -- legal action -- perhaps beginning with a letter from an attorney, setting a remedy deadline.
One more thought: You might ask the landscapers while they're there if it's possible to harness this unwanted flow to serve your purposes (property irrigation, pond, etc.)
Good luck. Hopefully, you can reach some (dry) common ground.
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