Tough question, but overall I'd say that the 'kill all the evil guys, because they are evil' philosophy may cause consequences for the paladin of Iomedae, especially if for example the evil individual surrendered or is a non-combatant. In my experience, the paladin who sees evil everywhere and smites without abandon is often a villain for the party to fight.
My reasoning is based around what happens in a later part of the "Wrath of the Righteous" Paizo adventure path, which is a high-level/mythic path:
In "Wrath of the Righteous", the players get called by Iomedae herself and asked a series of questions. The thing to note is the later part of the second question in the 5th book "Herald of the Ivory Labyrinth", (pg. 10): "...when evil assumes a fair form, and when weak villains beg for their lives, are they due mercy? Or are the wages of their villainy always death and oblivion?"
According to the book there is no true answer, and immediately answering "yes" or "no", causes consequences as a wrong answer. Iomedae seeks an answer that is hesitant or shows an sign of internal (personal, not party-based) conflict with the concept.
The non-spoiler version answer is; a Lawful Good person (which paladins are RAW), should temper rules with judgement. Thus someone who detects as evil should not be automatically killed for being evil. After all having an evil alignment is not inherently a crime (admittedly committing crimes may cause an evil alignment), and "He was evil" may not stand up in court.
Consider the possibility of turning a tool of evil into a tool for good; this is technically twice as good as just removing/destroying the tool of evil, as you make the force of good stronger. At the same time certain evil will not turn, may even pretend to want redemption; in which case it may be best to give said individual one chance, that is to say that if they betray your trust and later seek redemption, then it would be foolish to give another chance. Also consider the magnitude of the evil, so an evil baker isn't worth killing (albeit RAW, he probably won't have an evil aura, thus won't be picked up by detect evil), but some Demon/Devil Lord probably won't want to change sides, so it probably best to try to slay them.
Further more, Paizo's Faiths of Purity (pg. 26) outlined the tenets of a paladin of Iomedae as follows:
- I will learn the weight of my sword. Without my heart to guide it, it is worthless—my strength is not in my sword, but in my heart. If I lose my sword, I have lost a tool. If I betray my heart, I have died.
- I will have faith in the Inheritor. I will channel her strength through my body. I will shine in her legion, and I will not tarnish her glory through base actions.
- I am the first into battle, and the last to leave it.
- I will not be taken prisoner by my free will. I will not surrender those under my command.
- I will never abandon a companion, though I will honor sacrifice freely given.
- I will guard the honor of my fellows, both in thought and deed, and I will have faith in them.
- When in doubt, I may force my enemies to surrender, but I am responsible for their lives.
- I will never refuse a challenge from an equal. I will give honor to worthy enemies, and contempt to the rest.
- I will suffer death before dishonor.
- I will be temperate in my actions and moderate in my behavior. I will strive to emulate Iomedae's perfection.
Short Answer: A paladin must not be so bound to the concept of law that they lose sight of what it means to be good. So just because someone is evil, you don't have to slay them. A truly Lawful Good person needs to temper rules with judgement.