Let's look at this one step at a time, straight from the rules (well, the SRD):
"Detect Evil (Sp): At will, a paladin can use detect evil, as the spell."
"Detect Evil...You can sense the presence of evil. The amount of information revealed depends on how long you study a particular area or subject....
Lingering Aura: An evil aura lingers after its original source dissipates (in the case of a spell) or is destroyed (in the case of a creature or magic item). If detect evil is cast and directed at such a location, the spell indicates an aura strength of dim (even weaker than a faint aura). How long the aura lingers at this dim level depends on its original power...
Animals, traps, poisons, and other potential perils are not evil, and as such this spell does not detect them.
Each round, you can turn to detect evil in a new area. The spell can penetrate barriers, but 1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt blocks it."
"Mind Shielding: This ring is usually of fine workmanship and wrought from heavy gold. The wearer is continually immune to detect thoughts, discern lies, and any attempt to magically discern her alignment.
Faint abjuration; CL 3rd; Forge Ring, nondetection; Price 8,000 gp."
Okay, so definitely no detection of alignment. If the Succubus had only recently put the ring on (1d6 x 10 minutes or less), a lingering dim aura would be detected, but with no way to link that to the Succubus.
All this is assuming that you agree that detecting "evil aura" is essentially a subset of detecting alignment, which I think is indeed the case, especially as the related Detect Spells are:
Detect Chaos
Detect Good
Detect Law
I suppose you could make the case that this is not actually detecting the alignment, but only on aspect of the alignment, but that seems to me to really be splitting hairs.