Problem with updating set of values in custom field for all project by REST API

Hello

I am writing an integration module for our application that connects to our Youtrack. Its purpose is to keep up to date values in one of enum custom fields but I encountered a problem.

For now I've created an enum custom field "Company", filled it up with initial data, and added it to 6 projects. What I want to do, is to update its values using the REST API - and I actually managed to do that successfully, however values in project-specific custom fields that (I belive) use the same set of values didn't changed.

I am not sure if I explained my problem well enough, so I'll just write an example:

Custom Field "Company" initially containing 250 values is added to 6 different projects (from the admin panel). Then I run my application that uses REST API to insert new value into existing set of values (that is used by my custom fields) and, despite that in admin panel I can see new values in "Company" field, when I check on any issue in any Project using this field - there is no new values, only the initial 250.

What am I doing wrong and is there even a possibility to achieve that what I am talking about only by using REST API?