Any changes to schedules would normally be discussed at a site meeting between the involved parties.
These parties would include the client, contractor and sub-contractors, the architect and/or the consulting engineers.
In some instances variation orders (VO) will be required.
If the variation in the work is small, then to maintain goodwill it might be prudent to carry out the change, particularly if no extra time and cost is required.
In some circumstances this is not possible, and the main contractor or architect or other responsible person provides a variation order.
The purpose of the VO is to record the new agreement for the extra work to be done and any new costs incurred in completing the project.