Thomas,
[Aside from the trivial point that the terms convex and concave are typically used the other way around]: Your description does seem to indicate that job is being somehow 'pushed aside'.
As Jason and others have mentioned; the bottom of your cup [at a nominal 0.8mm] is rather thin … but I would still think that all you need is a decent tool, set at the right height, and square to the lathe's axis.
As John pointed out, you may find that your cross-slide is set to face concave, but this should only be very slight [almost immeasurable on a 28mm diameter], and certainly not what we are seeing. …. What does the face of the 'parent' material look like ? [sorry, already answered 'flat']
To help us solve your puzzle; could you please post a picture of the tool that you are using.
Thanks
MichaelG.
.
P.S. … My 'workshop' is currently in utter dis-array, so I can't offer any sort of demonstration; but [from the safety of my 'armchair'] I feel sure that one of our better organised members could easily part-off a 0.8mm thick disc of brass, as proof-of-concept.
Edited By Michael Gilligan on 12/08/2015 08:07:48