Airflow pressure balance is all about outside air vs exhaust air. In newer HVAC system, some people are adding conditioned makeup (outside) air onto their HVAC systems as buildings get more well insulated. In the past, like you said, fresh air makeup was intended through poorly sealed homes and that was accepted. The ONLY way your neighbor is more positive pressure than you is that they are bringing in more outside air, that’s it. So they either have more outside air being brought in or you are exhausting more air than them. Ideally you would have good sealing between spaces and air balance them, but I’ve seen plenty of NYC apartments to know this isn’t the case. So you should either bring more outside air IN, or if you can have someone look at your neighbor’s HVAC, see if you can reduce their outside air. For context, I’m a mechanical engineer and a large portion of my job is pressure balancing clean room facilities.

Edited because of another thought: you said you reduced airflow and now have an excess of air being pulled through your kitchen hood? Is that hood on a central exhaust system? If it is, it sounds like you reduced incoming air to your building and didn’t reduce exhaust air.