I have my Macbook set to require a password one hour after sleep or inactivity, but it still asks for my password even after a moment of sleep. Am I misunderstanding this setting or is there another setting I am overlooking?
There are a few things to consider with Macs and how they sleep.
You have display sleep, which is when the screen fades out.
You have computer sleep, which is when the system puts your work and settings in memory and draws a small amount of power; also known as standby.
Then you have deep sleep, which is when the RAM is stored onto the System's HDD. When you turn it on again, it will restore your session from disk to RAM. This process can take a while and you'll notice it more apparently depending on how fast your system is.
System Preferences > Security & Privacy > General there is a setting to
require password immediately after sleep, but this is only computer sleep, or soft sleep.
When your computer is in deep sleep, it will always require your password again when it wakes.
You may have encountered instant deep sleep without knowing, and this can be remedied by increasing the standby delay by following this guide here
You didn't say where you set the preference, or your OS X version.
System Preferences → Security & Privacy → General has a setting:
In OSX 10.9 / 10.10: "Require password Immediately after sleep or screen saver begins." In OSX Mavericks: "Require password for sleep and screen saver", followed by the time.
That item should be turned on and set to your preferred time.
If it already was, turn it off, quit System Preferences, then relaunch System Preferences and turn it on, then set your preferred time.