Supplements can have acne triggering ingredients. 

Common acne triggering ingredients in supplements are:

Iodine

Maca

Spirulina

Soy

Dairy

Vitamin B7 (Biotin)

Vitamin B12

Supplements with maca, iodine, spirulina, would likely affect your skin quicker, like within 48 hours. 

B7 & B12 behave a little differently in how they contribute to acne, so it could take longer to show an effect, and take a bit longer to work it out of the system.  Everyone is going to be different based on how their body absorbs nutrients, as well as what else is going on in their diet/gut health/what other nutrients they are taking in.  It also depends on long have they been taking acne triggering supplements.