Why do some games allow offline Steam achievements?

I know of another question where it is asked if you can get Steam achievements offline. The accepted answer to that was no.

But I do earn achievements for some Steam games while playing in offline mode!

For example, right now I am earning achievements for Cave Story+ as I play in offline mode. In other games I also earn achievements while playing in offline mode. Not just when I am disconnected but still in "online" mode as might be suggested in the linked question.

But what is really bugging me is that this does not happen with all games that have Steam achievements.

So, is allowing offline achievements something that Steam allows, the game devs allow, or is it something decided by a magical elf in the steam servers rolling some d20 dice around?

Edit:

As per request, I was able to attain visual evidence:

visual evidence

You should be able to see the achievement-get in action while in offline mode.

What is worth noting, (and something that I forgot to mention before) is that I only started earning achievements after I had went into online mode with the game installed. This is why I was able to earn this achievement with the ones after unlocked. I had started the game for the first time in offline mode, and did not notice that I was not earning achievements. When I had connected once, I did not have to start the game while online. I was able to earn achievements offline.

I also must state publicly:
I do not play on easy. This was for testing purposes only people. It was for Science!

steam achievements

Best Answer

There are three possibilities here:

Some games show that you've gained an achievement while offline, but when you connect back online, you will not see that achievement in your stats page, so you really didn't get credit for the achievement.
Some games store your achievement progress offline, and when you go online, it updates your profile and you get a whole bunch of achievements all at once.
Some games do not allow offline achievements at all.

Whether or not one of the three happens depends entirely on the game and the developers in how closely they integrate with the steam achievements.