In this case, the two feats are not actually interacting directly.
Deflect Attack simply grants extra chances for an Attack of Opportunity.
Evasive Reflexes simply grants you an alternate option to resolve a chance to make an AoO.
However, Deflect Attack has specific clauses detailing how you may use your AoO when an opponent attacks you armed or unarmed. With that detail, we follow the "specific beats general" ruling, and any AoO granted by Deflect Attack must be used to make a counterattack.
Regarding the question in the title, and the "general" question:
Yes, a feat can do that, if that is what the feat specifies that it does.
For instance, one of Elusive Target's options is "Negate Power Attack": after designating a Dodge target (the Dodge feat), if that target attempts to make a power attack against you they gain no bonus on the damage roll but still take the penalty on attack.
I managed to read the requirement for how Deflect Attack allows you to use your AoO like 3 times, and I still somehow managed to not actually process it until Simon pointed it out to me specifically. Thanks for catching that one!