For a suitable model $M$ for $Q$ and a condition $q \in Q$ we say that $q$ is *$(M,Q)$-generic* if whenever $r \leqslant q$, $D \in M$ dense, $D \subset Q$, $r$ is compatible with an element of $D \cap M$.

If $\lbrace p \in Q \cap M \colon q \leqslant p \rbrace$ is an $(M,Q)$-generic filter, then $q$ is called *totally $(M,Q)$-generic*.

$Q$ is *totally proper* if whenever $M$ is a suitable model for $Q$ and $q \in Q \cap M$, $q$ has a totally $(M,Q)$-generic extension.

A forcing notation $P$ is $\kappa$-distributive if the intersection of $\kappa$ open dense sets is open dense.

Now let $P$ be a totally proper forcing notation. Does it follow that $P$ is proper and countable distributive?

I know that the way back holds and want to know if it is equivalent.