As a DM, here's how I would approach this:
- Attitude is important. A great Good archmage summoning a demon to save a country is justifiable enough. If it's an exception for a significant reason, then it's just that - an exception. Sometimes, the ends justify the means (NPC organizations may disagree)
- Roleplay and remorse. A well-roleplayed good character would feel severe repulsion from the demon, disgust at their actions, and deep remorse afterwards. Lack of all of those hints at a necessary alignment shift.
- DM tools. The demon is bound, but by an inappropriate summoner. Maybe the summoning fails, or the demon turns side, or the demon is weakened and disjoints realities easily (See: Mordekaiden's Disjunction). If the "good" character persists, inform them that their control over the spell and the summoned demon grows. That the demon likes them more, the spell is easier to cast, and the creature is more powerful. If they are happy with this, it's time to review alignment
- NPC's. Any companion NPC's should notice the moral incompatibility and comment accordingly. World NPC's may comment on a newfound aura of evil, other mages will comment on lingering demonic spell traces and so on. Have the world respond accordingly, and judge the necessary changes by the player's reactions.
EDIT: Annendum, I am a big fan of corruption concepts as introduced by Warhammer (both) and Warcraft universes. The concept being that certain actions leave a lingering trace on your essence, and it's up to the individual's willpower/personality/conviction to either protect against them or embrace them. If defending, such defenses can fail when the pressure increases.
EDIT2: Read the OP more carefully, "neutral to evil". Neutral alignment is a complex concept, and TECHNICALLY shouldn't be intrinsically affected by summoning demons. If you like them, apply my personality/response/corruption concepts as appropriate.
I would.