Recombination thresholds in degree reduction of multiplied Shamir shares
This is the correct behavior. Since the degree of the multiplication sharing is $2t$, it will take $2t+1$ shares of either it directly or the subshares. If done on the subshares, the resulting sharing is of degree $t$. 

Shamir secret sharing is commutative with respect to polynomial evaluation.

Let $\sigma_1^t$ be the polynomial for sharing $s$ with degree $t$. So, multiplying shares generated by $\sigma_1^t$ and $\sigma_2^t$ (which shares some $s'$), we get a share of $\sigma_3^{2t}$, which shares $ss'$. To reconstruct $ss'$ it would take $2t+1$ shares.

In the degree reduction step, we create subshares with a threshold of $t$, or $\sigma_4^{t}\circ\sigma_3^{2t}$, in other words, we have a degree $t$ sharing of a degree $2t$ share. Due to commutativity, we can rearrange things to get $\sigma_3^{2t}\circ\sigma_4^{t}$, then apply the inverse operation $(\sigma_3^{2t})^{-1}$, to get $(\sigma_3^{2t})^{-1}\circ\sigma_3^{2t}\circ\sigma_4^{t}$, which gives you $\sigma_4^{t}$.

So I have probably thoroughly abused notation, but hopefully that makes sense. You are doing the inverse operation on a $2t$ degree sharing in order to get back to the degree $t$ sharing.

Some consequences of this are 1) in MPC we assume that everyone will participate in the protocol. If one party refuses to participate, the degree reduction won't work. 2) This is used to establish the theoretic upper bound on information theoretic honest-but-curious MPC protocols.