It's important to remember that each company establishes its own matching gift process. But in general there are two different paths for donors that most companies follow:

1. A donor submits their matching gift request electronically
2. A donor fills out their matching gift request using a paper form

Notification from matching gifts submitted electronically:
When an individual submits their matching gifts electronically using an online submission form (which Double the Donation often links to), the matching gift will be entered into the company's standard matching gift submission process.

In most cases the company will notify the nonprofit that an individual requested a matching gift and then ask the nonprofit to verify that the individual did in fact make a donation to the organization. This notification is done either through a paper letter to the organization or by email if the nonprofit has already created an account with the company.

Notification from matching gifts submitted using a paper form:
When an individual fills out a paper matching gift form, the standard process is for the individual to mail that paper form to the nonprofit. The nonprofit will then verify that the individual did in fact make a donation to the organization, sign the matching gift form, and then mail the matching gift form to the corporation for processing.

So yes, typically you do receive a notification but it's part of the standard company process which Double the Donation doesn't change and is not involved in.