Like the title says: the attacks are made with Magic Stone (cast by the Warlock, maybe even through the familiar) and thrown by their familiar itself.
Are those attacks considered attacks made by the Warlock themselves? If they are, do they trigger Hex?
I'm inclined to believe they are because the spell attack uses the Warlock’s statistics instead of the thrower’s.
Hex states:
Until the spell ends, you deal an extra 1d6 necrotic damage to the target whenever you hit it with an attack.
Since you and your familiar are not the same creature, the extra damage from hex does not trigger on your familiar’s attack. Your familiar is taking the Attack action and your familiar is making an attack roll, so it is your familiar that is making an attack. You, the warlock, are not taking the Attack action, and you are not making an attack roll, so you are not making an attack.
Hex gives the bonus damage only when you hit the hexed creature with the attack. Though Magic Stone specifies that the attack is made with your spell attack bonus, the language is clear that they are still the attacker, not you.
If someone else attacks with the pebble, that attacker adds your spellcasting ability modifier, not the attacker’s, to the attack roll.
The unwritten rule on spells is that they do what they say they do and nothing else. The description of Hex states:
(…)Until the spell ends, you deal an extra 1d6 necrotic damage to the target whenever you hit it with an attack.(…)
Note the bolded wording - the extra damage trigger when you hit the target. Not your familiar, not someone else holding your weapon and not someone else throwing a pebble that you infused with magic.
Magic Stone’s description says:
(…)You or someone else can make a ranged spell attack with one of the pebbles by throwing it or hurling it with a sling.(…) If someone else attacks with the pebble, that attacker adds your spellcasting ability modifier, not the attacker’s, to the attack roll.(…)
Magic stone allows someone else to make an attack with the pebbles you created and use your modifier for the attack instead of their own. They are still the attacker though, as they are the ones making the attack, the spell is explicit about it. Being able to use your modifier doesn’t change it in any way. Therefore, it doesn’t trigger your Hex because it’s not your attack.
Finally, Pact of the Chain has no impact on this. All it does is allows you to learn the Find Familiar spell when it is usually only available for Wizards, gives you a few unusual choices of the familiar’s form and allows your familiar to Attack with its reaction. None of this interacts with Hex and neither do any of the standard actions that a familiar can perform.
