The amount of time a domain will take to start working varies depending on the change that has been made. If a DNS zone record (such as an MX record) was updated then the domain will usually take between 2 and 8 hours to start using the new record. If the nameservers were updated however the change will often take longer, generally up to 24 hours but in rare cases it may be longer.
The above will generally depend on what the TTL (Time to Live) was set to. Effectively, the TTL tells your internet provider how often it should check the domains DNS to see if it was updated. If this is set to 86400 then they should check once a day. Lowering the TTL prior to a DNS change in general will ensure that DNS changes happen quicker, however the TTL change should be changed at least a day prior to the DNS change or it will have no effect.
If you require further information to the above, please submit a ticket via your client area and a member of the team will be happy to advise.