I've never found any benefit from Schräder-to-Presta adapters other than that reduce the amount of stuff getting into the rim via the gap around the valve.
even assuming the normally expected usefulness of the adapters, it's hugely unlikely that it would have anything to do with your issue.
I'd be more inclined to suspect that you have the reinforced part around the valve trapped underneath the bead. After having installed a tube, but before inflating, make sure the valve is free to move inside the tire.
Failing that, some tires are a bit tight, and will need some encouragement to settle out to the hooked edge evenly all around.
And, from afar, I can't entirely rule out that your tire is damaged or defect.