i am doing fixed period. membership start date is May 1, 2019 membership end date is April 30, 2020. Early bird registration starts March 1, 2019. I have set the Fixed Period Start Day to be May 01, anticipating May 1, 2019 I have set the Fixed Period Rollover Day to be March 01, anticipating March 1, 2019. I anticipate membership end date to be April 30, 2020, which it is. I anticipate membership start date to be May 1, 2019 which it is not, it gives me May 1, 2018.
Yes this is an aspect of / issue with Rollover - ie when someone signs up, civimember effectively gives them the start date of the membership cycle on the day they sign up, and then adds on the extra year. so yes seeing 'start date' of 1 May 2018 for someone signing up on 5 March 2019 fits with the civimember logic.
i don't say i necessarily like what it does but the logic is consistent but means that you may need to pay more attention to the Join Date than the Start Date.
That is, assuming everything else looked right, ie End Date was 30 April 2020