What is the correct order to both marinate and velvet the meat? Velveting a meat is a Chinese technique to coat meat with oil and egg whites and can prevent overcook. In the process, it needs to be left for about 30 minutes in refrigerator for the coat to apply then stir the meat in simmering water for about a minute. The meat then is ready to be used for anything else.

The problem is, I wanted to also marinate the meat in mixture of sauces, salt and pepper. When should I put the marinate into play? At the same time as the 30 minutes refrigerator? (That would make the meat not versatile to use in other dishes, as the sauce applied is specific to a dish I wanted to prepare.) or after the 1 minute stir? (I worried that this would somehow destroy the velvet effect, or not?)
Be sure to look at this related question too: How does velveting work?

Serious Eats just kind of took this on. They added some nice flavor to the velveting marinade, and then sauced the chunks after cooking. Some kind of adaptation of that concept would probably work well for you.

I have done some small experimentation with adding flavors to the egg/cornstarch marinade, and so far I haven't had any problem. As long as you've got enough egg white and cornstarch to make a light batter, you can add other things for flavor. BTW, the flavor of the velveting recipe in the question I linked to is lovely.