Help! Just a little question.

I finished my company hunt log and now I want my minion. How do I get it or where or who do I go see.

umm Í think you mean the buyable one? the grand company sells it at their headquarters..where you apply for promotions

when I look at my achievements it shows a treasure box and shows the minion. Maybe they are saying I can buy it now?

There's a guy near Apkallu Falls in Old Gridania. I forget his name but if you talk to him he gives you all your achievement rewards. The closest aethernet shard to him is the Amphitheater one

You get a puppet minion for finishing the GC log.
You have to speak to the achivement NPC near a little area of the Old Gridania map called Apkallu Falls; it's where the 2 paths converge north of the amphitheatre/delivery moogle area.

Thank you for helping me.