You know your system better. I run veg nutrients for the first 2 weeks, basically until I have a good bud set and the stretch is slowing, and then switch over to my flowering nutrients. I normally start getting buds to show at around day 4-10 days. I have a range of plants from 8-11 week flowering times, and they all show within a week, I don't know where this 3 week nonsense is coming from. I mean if you are running some crazy 20 week flowering sativa, then maybe it takes 3 weeks for them to show, but anything from 8-12 weeks should start budding within a week of flowering.
I do use a bio stimulant (BioBud from General Organics.) I give it to them a week prior to flowering, and until I have a good bud set, and then I switch over to BioBoost by BioCanna. I definitely do see a lot shorter time of onset of flowering when using this. I have used with and without and I normally cut the time it takes to start flowering in half.