Solving a big matrix DE system using NDSolveValue

I know there are similar questions, but I was unable to understand the solution for my case in any of them.

I have the following:

Commutator[a_,b_] := a.b - b.a;

initialstate = {0,1,0};
pin = KroneckerProduct[Conjugate[initialstate],initialstate];

pI = NDSolveValue[{
p'[t] == - Commutator[p[t].F1[t], L[t]] + Commutator[ConjugateTranspose[F1[t]].p[t], ConjugateTranspose[L[t]]]
- Commutator[p[t].F2[t], ConjugateTranspose[L[t]]] + Commutator[ConjugateTranspose[F2[t]].p[t], L[t]],
p[0] == pin
},
p,{t,0,1}]

It might be relevant to say that F1(t) and F2(t) are both numerical 3×3 functions and L(t) is a big analytic 3×3 function.

I have seen in other posts that the sum will act before the dot operators causing Mathematica to misinterpret what I am trying to calculate. It indeed returns me an error if I try to execute it, so what the correct syntax for this problem is? Where I have dot operators not only in the DE system but also inside the Commutator function.

I would really appreciate it if, besides the solution, you could provide me an explanation of what is happening.