Navigation flow across multiple websites

I'm working on an authentication flow for a product we're creating. When someone signs up for our service there are a few steps someone has to take;

1. Go to our website
2. Click 'sign up'
3. Complete sign up form

After that the user goes straight to the product. There are three pages, one per step. The website (1), the sign up page (2) and the product (3). These three pages are part of two websites, the commercial website (1) and the product website (2 and 3). Because of this, the pages have a different look and feel. The commercial website (1) is designed to inform and for users to sign up. The sign up page (2 and 3) is very clean, focussed on the form and the product.

So the user first sees a website in one style and after that pages in another style.

Question

Is it good practice to let users take big steps in a flow, from one website to another?

I can imagine that users might feel lost or suspicious when the next step in a flow is part of another website.

Note; this question could have some overlap with the graphic design stack exchange, but my question is directed at the ux of taking steps across different styles.