new-jersey
Your Responsibility
As a general rule, if you develop a property, you need to control the stormwater that your property generates in a manner that conforms with the requirements of NJAC 7:8.
The initial promulgation of these rules occurred in 2004* and required all Major Development** of a site after that date to control runoff from disturbed areas to conform with, among other things, runoff rate. Meaning, if your lot already discharged a peak rate of 3 cubic feet per second (CFS) from a storm with a 1% recurrence interval (i.e. a 100-year storm), you would be allowed to continue to discharge towards that lot provided you conformed with NJAC 7:8. Without getting into the technical nature of NJAC 7:8 says, you could at most have a peak discharge that matched existing.
Notably, the rule does not require you to conform with the rules if you're not doing anything that triggers the Major Development threshold. This means that there is a degree of implicit permission to increase stormwater towards a neighbor, but the triggers for Major Development are generally low so it's unlikely you'll be able to increase it very much.
It is possible for local municipalities to have additional requirements which may apply to home improvement projects and sometimes those rules include storm controls. Those might have applied to the installation of the gutters, but you'd have to check your local codes. Regardless, it's unlikely that your project substantially altered the drainage patterns (i.e. if 1,000 SF of impervious roof was going towards your neighbor before the gutters and now due to the gutters it's 1,100 SF of impervious roof, it's not likely to be making a ton of difference).
Other Factors
Finally, let's focus on your neighbor's responsibilities. When he purchased his house, he certainly had the right to inspect the landscape and observe whether or not there was the potential for poor drainage conditions. If he felt unqualified, the purchase of all homes in NJ requires a survey of the lot to determine the property corners, but he could've also paid the surveyor to pick up and show topography (I did).
As an additional point of discussion, it's also possible that climate change is worsening storms in your area. Updates to NJAC 7:8 have had an eye towards increasing the intensity of the design storms in order to address issues with previous storm controls being underdesigned. A primary driving factor for this stems from the fact that NJ has been hit with multiple 500-year flood events since 1999 which from the regulators' point of view suggests that '500-year flood' is a misnomer (more than it already is).
The practical effect of these more intense storm events is that flooding may occur in areas where it didn't before. If your neighbor's lot has a low lying area with generally well draining soils, they may've not had an issue before. However, if due to climate change you regularly have multiple rain events in a row, the soil will become saturated and eventually be unable to receive any additional runoff and thus begin to pond. While this sucks for your neighbor, that's climate change. It usually sucks.
*This link is to the current iteration of the rules which went into effect in 2023. The differences between the 2004 and 2023 version are substantial from a technical point of view, but generally irrelevant for the purposes of answering this question.
**Major Development is a specific term defined in NJAC 7:8-1.2 and has expanded with later iterations of the rule. But the short version is that if you develop your lot in a manner that either disturbs more than an acre of land or constructs 1/4 acre or more of impervious surface, then the rule applies to you.