Immediate means immediate. There is no reason why you would wait until next round or let the effect take effect for any amount of time before allowing the second save.
Character would roll the save initially, then if it failed, roll a second save to see if it takes effect or not.
The paladin in our group was targeted by a suggestion spell from an evil caster. He failed the save for it. He immediately demanded a new save quoting the second part of the pfe spell, using the morale bonus instead of the resistance bonus from the first section of pfe. After reading the spell and seeing that it is different than the 3.5 version and before versions, I was kind of lost as to if he would get another save in the same round. I gave him the benefit of the doubt but had him bet 100 xp on the outcome of this question. I would like a ruling as to whether he would get another save in the same round.
I assume from the text he has a Protection from evil effect going before the spell is cast.
This spell wards a creature from attacks by evil creatures, from
mental control, and from summoned creatures. It creates a
magical barrier around the subject at a distance of 1 foot. The
barrier moves with the subject and has three major effects.
Fluff not relevant
First, the subject gains a +2 deflection bonus to AC and a +2
resistance bonus on saves. Both these bonuses apply against
attacks made or effects created by evil creatures.
Paladin gains a +2 resistance bonus, and +2 Deflection bonus to AC against evil spellcaster
Second, the subject immediately receives another saving throw (if
one was allowed to begin with) against any spells or effects that possess or exercise mental control over the creature (including enchantment[charm] effects and enchantment [compulsion] effects such as charm person, command, and dominate person).
This saving throw is made
with a +2 morale bonus, using the same DC as the original effect.
If successful, such effects are suppressed for the duration of this
spell. The effects resume when the duration of this spell expires.
While under the effects of this spell, the target is immune to any
new attempts to possess or exercise mental control over the target.
This spell does not expel a controlling life force (such as a ghost or
spellcaster using magic jar), but it does prevent them from controlling
the target. This second effect only functions against spells and effects
created by evil creatures or objects, subject to GM discretion.
This part applies only if the paladin was "Affected" by a spell before the Protection from evil effect was placed on him. He gains a new save at +2 to suppress the current spell effect. If the save fails the enchantment is still in effect.
If the suggestion was cast after the Protection from evil effect was placed on him he is immune, note above bolded text
Third, the spell prevents bodily contact by evil summoned
creatures. This causes the natural weapon attacks of such creatures
to fail and the creatures to recoil if such attacks require touching
the warded creature. Summoned creatures that are not evil are
immune to this effect. The protection against contact by summoned
creatures ends if the warded creature makes an attack against
or tries to force the barrier against the blocked creature. Spell
resistance can allow a creature to overcome this protection and
touch the warded creature.
Not Relevant
Very good point about the immunity, didn't read past the first part ;)
The immediate roll would be when the Prot spell comes into effect assuming the offending effect was already in play.