I can see "use evocation foci" as an interpretation of "the spell is cast like evocation," but since it then goes on to explain that as "power first, control later, all done in one exchange", I don't find that convincing.
Evocation uses
Power and control. Thaumaturgy uses
Complexity and Control. Therefore evo-thaum uses evocation foci because complexity won't boost an evocation spell - only power does that.
The difference between evocation and evothaum is the "elements". For example, evocation lets youyou can attack with spirit, fire, water, earth, air.
Evothaum lets you attack with biomancy, ectomancy etc... it's still an attack but it has a different narrative and, in some instances, might have different effects.
Evocation lets you put up a block while evothaum lets you put up a ward. A ward has different limitations and advantages than a block. The
methods are all evocation. Evocation does not use thaum foci.