For those who are still looking for a way to limit Deployment to users.

The limitation is implemented by checking conditions in the deployment steps, to change the list of users:

1. Go to the Build Step settings: SSH Exec :
   URL Teamcity>/admin/editBuildRunners.html?id=buildType:<ProjectName> and go to edit settings:
   Image Step 1

2. Go to add/editing conditions:
   Image Step 2

3. Let's bind to a system variable - the login of the user who called the Deploy event. Set:
   Parameter Name: teamcity.build.triggeredBy.username
   Condition: matches
   Value: .*(,|^)(admin|user2|user3|user4)(,|$).*
   Image Step 3

4. Save

5. Testing