```python
from typing import List

def install_order(packages: List[str], requires: List[List[str]]) -> List[str]:
    """
    Determine the correct installation order for packages given their prerequisites.
    """
    if not packages or not requires:
        return []

    # Validate input
    if len(set(packages)) != len(packages):
        raise ValueError("Package names must be unique.")
    
    for pkg, needed in requires:
        if pkg not in packages or needed not in packages:
            raise ValueError("Package names in requirements must exist in the list of packages.")
    
    # Build dependency graph
    needs = {name: 0 for name in packages}
    enables = {name: [] for name in packages}
    for pkg, needed in requires:
        needs[pkg] += 1
        enables[needed].append(pkg)

    # Detect cycles
    visited = set()
    stack = []
    def has_cycle(node):
        if node in stack:
            return True
        if node in visited:
            return False
        stack.append(node)
        for neighbor in enables[node]:
            if has_cycle(neighbor):
                return True
        stack.pop()
        visited.add(node)
        return False

    for pkg in packages:
        if has_cycle(pkg):
            raise ValueError("Requirements form a cycle.")

    # Topological sort
    ready = [name for name in packages if needs[name] == 0]
    order = []
    while ready:
        next_name = min(ready)  # Use min to ensure alphabetical order
        order.append(next_name)
        ready.remove(next_name)
        for follower in enables[next_name]:
            needs[follower] -= 1
            if needs[follower] == 0:
                ready.append(follower)

    return order
```