When to unit-test

We have built a small custom website using a very popular framework. The project is small basic crud-application that allow users to upload pictures into their private image galleries.

The project is so small that any experienced developer should be very comfortable doing it alone in about 250 hours.

The client was on a tight budget.

1. Should unit tests always be written during first phase of development, or is it safe to say that it's acceptable to write unit tests before we start improving on the project?

2. Would unit testing while developing the first phase contribute to the overall cost for the client in phase 1? We're using a combination of Doctrine, Symphony, TWIG, requirejs, jQuery and other tools.

Basically; the client is complaining for lack of unit tests, while we feel that we simply postponed the additional cost - in benefit of the client. The client is now making money on the project, and can afford to pay for writing the unit tests. He is now trying to get the unit tests for free.