I'm a bit confused here. Since the Eidolon and Summoner are fused together as a Synthesist, could I apply an evolution like reach to one of my Summoner's own natural attacks? Or would I have to wait until level 10 to use Aspect?
You have access to all your own and your Eidolon's attacks.
From the Synthesist's Fused Eidolon class feature:
The synthesist uses the eidolon’s base attack bonus, and gains the eidolon’s armor and natural armor bonuses and modifiers to ability scores. The synthesist also gains access to the eidolon’s special abilities and the eidolon’s evolutions. The synthesist is still limited to the eidolon’s maximum number of natural attacks.
You can still use your own Natural Attack(s) while Fused, but you cannot do so beyond the normal Eidolon limit on Natural Attacks.
However, you cannot apply Evolutions to your own attacks.
The Reach Evolution must be 'attached' to a Natural Attack selected for your Eidolon. You (the Summoner) don't have Evolution Points to spend, your Eidolon does. You must select something your Eidolon has. Ref:
One of an eidolon’s attacks is capable of striking at foes at a distance. Pick one attack. The eidolon’s reach with that attack increases by 5 feet.
Using Aspect does allow what you want.
You would be able to select your own Natural Attack with the Evolution Points diverted by Aspect. The Reach Evolution has no requirement that you wouldn't qualify for.
While the synthesist and eidolon do fuse, they're still separate entities as far as evolution points are concerned. The eidolon's evolution points can only be spent on the eidolon, with the exception of the aspect ability.
Additionally, since the eidolon effectively replaces the synthesist's physical body while fused, you won't be able to use your summoner's own natural attacks while the eidolon is summoned. You'd have to apply the reach evolution to one of the eidolon's natural attacks, and attack with that instead.