There are a lot of theories about autos and flowering and tap roots and such. Almost all of those theories are false. I have seen autos grown in solo cups full of roots and not go into flower until long after transplant, autos grown in really tall home-made air pots where the tap never hit the bottom, and have grown many autos myself that go into flower regardless of where their roots are at the time.I was reading that you can extend veg in an autoflower by not 'constricting' the roots. Usually extend veg by two weeks. Supposedly, when too many roots hit the side of a fabric pot it triggers flowering - so more room gives more veg time.
Autos go into flower when their internal clock says it's time. High stress (like excessive heat) can send them into flower early, but roots don't seem to be a consistent trigger.