Contact calling is difficult to manage and there are different strategies. What I do is call back in a soft voice. My birds call because they view me as their flock and are concerned or worried where I have gone.. So I think it is kinder, for the birds, to call back.
I do not live in an apartment, but the neighboring house is pretty close and windows are left open a lot in the summer. Thus far no issue and I have 2 parrotlets and a plumhead. My neighbors didn't know I had birds until I asked them. Parrotlet voices can be noisy at times, and they shouldn't be underestimated, but they are actually much softer spoken than other species. Can you ask your neighbor if they hear your bird? They may not even know you have a bird and it might bring you peace of mind to know it doesn't bother them. Or if they say, 'Hey yeah that bird is a little bothersome.' Well then you know and we can think up some ideas for noise dampening that can help you live in a harmonious home. Birds will make noise, and you should embrace it as a sign of content and happy birds. Adding more fabric materials to your room in the short term can absorb some of the sound.