If I donated Tuesday at another plasma center will I have to wait a week before I go in to this donation center and become a new donor

U would have to wait until next week to donate again..

Yes. You cannot donate at 2 different centers. They mark your finger.

You can only donate twice a week, regardless of what center. So if you donated Tuesday, and let’s say Thursday- you couldn’t become a new donor at Biomat until Tuesday in order to not violate the 2x rule. Most centers advise against donating with two centers.