Evaluate

u[x_]:=x

r={x->a+b}

uu[a_,b_]:=Evaluate[u[x] /. r]

uu[1,2]

Invece   . . .

uu2[a_,b_]:=u[x] /. r

uu2[1,2]

. . .   ma  . . .

uu3[a_,b_]:=u[x] /. x->a+b

uu3[1,2]

?Evaluate