Insurance purchased @ 12:08pm which was meant to begin immediately at the next interval (every 15mins on the hour) so at 12:15pm I would of been insured however it seems like my partner selected 12:30pm in error.
I am not sure what you mean by "meant to begin" in assocation with the start time, but there is a potential issue in this area.
There is presumably some widget in the UI which is some sort of clock defining the start time to a 15 minute granularity.
Is it pre populated in any way or do you have to select it.? You should be able to figure this out with a few tests. (If it were my design it would most likely to always force a use selection for a number of reasons).
There is also a further consideration. By the time the various operations have been completed (some of which involve indeterminate waits for user input and external 3rd party systems) is this time still valid? If not what does it do ?
You should be able to ascertain this to an extent with personality testing.
It is far from impossible that a system proposes 12:15 and subsequently changes that to the next 12:30 point because 12:15 had already passed by the time the payment was confirmed by an external processor.
A GDPR request for all the logs and times both to the insurer and to the provider of the payment method may provide some useful information.
Analysing and utilising it would be a different thing of course.
A scenario to try and figure is:-
Start applying at 12:08, set time to 12:15, submit for payment before 12:15, complete payment after 12:15. There are a variety of scenarios that would be worthwhile to ascertain the what the result is. The 3 anticipated outcomes would be refusal and refund. Start at 12:15 even though that predates completion. Start at 12:30, either with notification of change or without.