As per the CM document Administering Avaya Aura™ Call Center Features on page 111:
https://downloads.avaya.com/css/P8/documents/100082001
If you add or change skills on the switch, the agent must log out and then log in again before the changes take effect. This means only after an logout and login back then the agent skill set can be reflected with the new skill set.
And in the Avaya Call Management System Administration on page 144:
https://downloads.avaya.com/css/P8/documents/100114778
Skill changes take effect immediately for agents who are in AUX work mode, AVAIL (available), or logged out. Changes are pending for agents on calls or in ACW work mode until the agent enters the AUX work mode, becomes available, or logs out. Because of this, agents who frequently have calls on hold may have skill changes remain pending for a longer time than expected.
When CMS supervisor send the skill change request, CM will automatically make the agent logout/login to take effect the new skill set as long as the agent is not on call or ACW work mode, and this action is very quick and there is not any effecting with the agent,