I'm brand new so not entirely sure, but like you I saw this info and had 12 attunement but only one slot. So I looked around more. According to a separate site (darksouls3.com) the additional slots come in at higher intervals than what's said here, i.e., the next #2 slot would be at 14 instead of 12: 'Extra Attunement Slots come at Attunement level 10, 14, 18, 24, 30, 40, 50, 60, 80 and 99.' Dark Souls 2 has a new emphasis on dual-wielding weapons, and this is the best class for taking advantage of the new mechanic. The swordsman is also pretty nimble, so rolling is pretty effective.

In-Game Description

Dark Souls 2 Attunement Slots Rings

Attribute governing number of spells that can be attuned. Boosts spell-casting speed.

Use

• Increases the number of Attunement Slots available for Sorceries, Miracles, Pyromancies, and Hexes.
• Main stat for increasing Casting Speed. Its effect is double that of Intelligence or Faith.
• Increases Curse Resist alongside with Adaptability.
• Secondary stat for increasing Agility.
• Increases number of spell casts. The amount of the increase varies between spells.
• Slightly raises HP.

Attunement Slots

Equipment which increase Attunement Slots

Equipment which increase Spell Casts

Equipment which restore Spell Casts

Note: Saint's Hood, Hexer's Hood and Northern Ritual Band all work in the same way. Spell uses are being multiplied by 1.1 (1.2/1.3 for the +1/+2 versions of the ring respectively) and then rounded up. For example, having a spell with only one use, the number will increase from 1 to 1.1, then be rounded up to 2, resulting in two spell uses.

Dark Souls 2 Adaptability

If you combine one of the hoods with the Northern Ritual Band, the spell use percentage will stack additively (10% + 10% = 20%, or 30%/40% for the +1/+2 versions of the ring). This means that, upon using both the standard version of the ring and one of the hoods, a spell with one use will increase its number from 1 to 1.2, then be rounded up to 2, resulting in two spell uses. However, using both on a spell with six uses, it will increase from 6 to 7.2, then be rounded up to 8, resulting in eight spell uses.

Spell Casts

Dark Souls 2 Attunement Slots Ring Toss

Depending on the spell, it may start with 1, 2, 3, 4, 6, 8, 10, 15, 20, or 30 casts at base Attunement.
The table below shows how many casts become available with increased Attunement ('-' is used to indicate no increase from previous cast amount).

Dark Souls 3 2 Attunement Slots Ring

Dark Souls 2 Attunement Slots Ring Quest

Note - Spells that start with 2, 3, or 10 casts can increase by different amounts. While there are two spells (with 1 cast each) that does not increase in casts (you can use equipment to gain more casts of these though).