I think those tyres must be slightly undersize. Tyres often are now, as an insurance against blow-offs. When you inflate the tyres, they should stretch enough for the beads to pop up onto the bead seats (those raised edges of the rim well). Sometimes they need help.
That it’s the same problem section on both tyres could be due to the manufacturing process leaving a kink in the steel bead wire, or perhaps its rubber coating is a bit stickier in that place. Whatever, the first thing is to reduce friction between bead and bead seat. Ordinary talcum powder is usually effective. Apply plenty to the edges of the tyre and inside the rim, then inflate to maximum pressure.
If you don’t have a pump with a gauge, you’re probably running your tyres much softer than you think and simply inflating to maximum will probably seat the problem section with a satisfying pop! If it doesn’t, over-inflate by as much as 50% until it does, then let out the excess.
If that doesn’t work, use a more slippery lubricant. Deflate the tyre, ease the problem side back from the rim flange and squirt concentrated washing up liquid into the gap. Work it all around the bead and bead-seat with a finger. Then inflate again.
Once a tyre has popped into place, subsequent fittings should be easier. If these methods fail: reject the tyre. It won’t be the rim.
This was first published in the August / September 2014 edition of Cycle magazine.