Tangent measure to $\delta_y$.

Question

I don't know anything about geometric measure theory but I was watching this video to try to understand the concept of tangent measures. I read that if $\mu=\sum c_i\delta_{y_i}$, then $Tan(\mu,a)=\{c\delta_0:c>0\}$. So I try to prove this. for simplicity I just start with $\mu=\delta_y$. Then take $\phi$ supported in $B(0,1)$ for example then $d_i\int\phi((x-a)/r_i)\delta_y(dx)=d_i\phi((y-a)/r_i)$. Then if taking appropriate sequence $d_i$ and $r_i$ this seems to converge rather to $\phi(a)=\int\phi d\delta_a$ no? So wouldn't the tangent measure be $\delta_a$? Was this a typo or did I make a mistake?