Yes. How is that confusing? There are ten perk options for each SPECIAL stat, one for each point. If you start with 1 AGI, you have access to the tier 1 perk. If you start with 2 AGI, you have access to tiers 1 and 2.
Are you asking if you get the perk or have access to it? SPECIAL points only give you the option to spend a perk point on a certain tier of perks. If you have 7 AGI, you have access to the tier 7 perk in the AGI tree, but you still need to spend a perk point to actually obtain the perk. You don't need 2 AGI to obtain the tier 1 perk.
The Fallout wiki is a great source to check out what kind of character you want to build. http://fallout.wikia.com/wiki/Fallout_4_perks
I already know that I want to build an Intelligent and Charismatic character
Also, you don't need to take tier 1-5, in order to take the tier 6 perk for instance. You can go straight for Tier 6 if your SPECIAL stat is high enough and you have a perk point to spend.
Each perk also has multiple levels, just like in the old games.
I think the OP has he system a bit confused. First off, it's not a skill tree but a perk matrix (SPECIAL attributes at the top and Stat values down the rows). You do NOT have to learn the perks in any order. You just have to meet the requirements and have a perk point to spend.