The way I look at it is that Summer magic is an element of its own that overlaps with other spellcasting powers. In your example, it's almost as if the character now knows evocation elements from two different styles of magic -- three from the 'classic' style (fire/earth/water/air/spirit) and one from the 'Fae' style (summer/winter/spring(?)/fall(?)). In addition, the character knows a specialized 'theme' of Thaumaturgy as part of Summer magic in addition to any other themes and functions he already knows, and can cast that theme as though it was evocation.
There is some overlap in both categories. As such, when choosing specializations or focus item, I think that "Summer Magic" is an option, which overlaps other options but does not stack. That is, you can cast a flame attack as either a Fire element evocation, or as a Summer magic evocation, or as a Fire element evocation powered by Summer (which would generally be the most effective because it gives all of the benefits of fire and summer). You could have a +2 fire power and a +1 summer power, but you can't use both bonuses on a spell. Instead, you'd use the best that applies to the spell cast. For a flame bolt spell, that could be either. For a plant growth spell, it would have to be summer rather than fire.
As another example, if you had +2 fire power and +1 summer control, you could cast a summer-powered flame bolt using the power bonus from fire and the control bonus from summer. (But the plant growth spell would benefit from only the summer control bonus, as before.)
I think that Summer magic is still split into Evocation and Thaumaturgy for purposes of specialization and focii. Summer Thaum cast as an Evocation would count as an Evocation for purposes of bonuses, while ritual uses of Summer magic count as a 'Theme' within Thaum. So if you had a bonus to a functional aspect of Thaum (like Crafting) it would give bonuses to Crafting items with Summer magic, too. Or if you had a bonus for a Thaum theme that overlapped with Summer magic (like Biomancy), then you could use which bonus was better, so long as the effect you want is covered by both themes.
At least, that's my take. Assuming it even makes sense to you.
