I understand why you are worried. The short answer is that an urban planter box can leak water onto the balcony below, but it does not have to. Most problems come from drainage holes, overflow, overwatering, a missing or cracked drip tray, condensation, or a damaged reservoir. A well-designed self-watering planter with a sealed reservoir and a fitted saucer is much lower risk, especially if you test it before planting and maintain it carefully.
To protect your neighbor and your relationship with your landlord, treat water management as part of the setup, not an afterthought. Choose a planter with an integrated reservoir or a closed base, and always use a drip tray under any drainage holes. Place a waterproof mat or shallow tray under the whole planter, and raise it slightly so air can circulate and leaks are visible. Before adding soil, fill the reservoir and run water through the system on the balcony to check for drips. If you see any water underneath, fix it before planting. Avoid overwatering; water until the reservoir is at the recommended level, not until water runs out the bottom. Empty saucers after heavy rain, and check the planter after storms or hot weather, since heat and expansion can stress plastic parts.
Also think about placement. Keep the planter away from the balcony edge and any gaps between railings, and make sure it does not block the balcony drain. Use lightweight potting mix rather than heavy soil, and avoid hanging planters unless they are rated for the load. If you rent, it is wise to tell your landlord what you plan to do and show them the drip tray or waterproof mat. A short message like "I am planning to use a self-watering planter with a sealed base and a drip tray; I will test it for leaks and check it regularly" can prevent misunderstandings. Check your lease or building rules too, because some buildings restrict balcony planting or require waterproofing.
In practice, the risk is low if you use the right container and inspect it often. Check the tray, reservoir, and base every week, and replace cracked parts immediately. If water ever reaches the balcony below, stop using the planter, apologize promptly, and document the issue. With a sealed system, a drip tray, a waterproof mat, and sensible watering, you can enjoy your urban planter box without making your landlord upset or damaging the balcony below.