It’s not really a hidden markov model unless there are time dynamics in the probabilities of getting one shock or the other, no? From what I understood, there’s no transition probabilities between the two shocks, it’s just a static probability of getting one or the other.
I don’t think the top row of R should be zeros. Substituting everything gives:
a_t = \rho a_{t-1} + \eta_{t-1} + \varphi_t \epsilon_{t,1} + (1 - \varphi_t) \epsilon_{t,2}
Setting the top row of R to zero would wipe out the time t shocks in a_t.