Well, Red Bull is not a customer team. Although they do have Renault engines (is that what you mean?), the chasis is pure Red Bull. Same for McLaren. A customer team is like (looking back) Merzario and Rebaque, they had chasis AND engine from an already built up team. Didn’t Spyker also have a customer car, man, forgot….
I was thinking about this and I can’t actually think of a team that won either Championship whilst being an engine customer of a manufacturor that had a full works team at the time. Red Bull or McLaren could become the first