In the past they've either sent me an SMS or called me -- after it clears, you still need to instruct them to deduct the miles and issue the upgraded ticket.

Assuming these segments are the outbound/inbound of a roundtrip: If you've already confirmed the upgrade on one segment, they should have deducted at that time the one-way mileage for that upgrade, and will deduct additional miles if/when the next segment clears. The total mileage you owe will be the amount for a roundtrip. My experience has been that they deduct only enough miles to make up the difference between the one-way they've already ticketed and the roundtrip, although others have reported that they'll deduct another one-way and then refund you back the difference.

If it's for two connecting segments on a one-way, I'm not sure how they handle it.