Basically "Thaumaturgy at Evocation Speeds and Methods" adds a certain type of Thaumaturgy as an evocation "element"
Evocation Methods include:
Conviction limiting base power (overcasts are possible of course, but incur extra stress)
Rolling Discipline once to control said power.
So, those spells work like any other evocation, they simply have a different scope of effects.
Lore looses influence on said spells when cast at evocation speed.
Example:
Thaumaturgy (Divination) at evocation Speed and Methods. (Conviction 5/Discipline 5)
A Tracking spell with power 5 can be cast for 1 mental stress.
With Overcast, a tracking spell with power 7 can be cast for 3 mental stress.
Now, if the caster has a Thaumaturgy specialization in divination, those bonuses add into casting said spell, whether they are cast as evocation or thaumaturgically.
A +2 complexity bonus on thaumaturgy (divinations) would allow for the aforementioned tracking spell with power 7 to be cast for 1 mental stress.
Regardless of power, be it overcast or "safe" powerlevel, as an evocation the spell must be controlled with a single discipline roll.
Also, you still need a symbolic link to cast certain spells, you simply don't need the whole circle/ritual dance to perform it.