I am assuming that you are referring to the comment on page 9 of this paper. Indeed, given a pseudorandom $x\in \mathbb{F}_{p^r}$, you can parse it as a pseudorandom $\vec x \in \mathbb{F}_{p}^r$, and re-interpret the additive shares of $x\cdot \vec u \in \mathbb{F}_p^n$ as shares of $\vec x \otimes \vec u \in \mathbb{F}_p^{n\cdot t}$.
Now, if you do a VOLE over $\mathbb{Z}_{2^k}$, you can perfectly use $\vec x\in \mathbb{Z}_{2^k}^r$ to get shares of $\vec x \otimes \vec u$ over $\mathbb{Z}_{2^k}^{r \cdot n}$. This does not even use subfield VOLE (which, here, would actually be subring VOLE, since we're not working over a field). Indeed, this is simply doing $r$ parallel VOLEs with receiver inputs $x_1, \cdots, x_r$, fixing a sender vector $\vec u$. Our construction easily allows fixing the vector $\vec u$ across multiple instances, so nothing goes wrong here.
Regarding security, however, a word of caution: the space where you generate the VOLEs is tied to the underlying assumption. When generating VOLE over $\mathbb{Z}_{2^k}$, you end up with a construction that is secure under a variant of the LPN / syndrome decoding problem over the ring $\mathbb{Z}_{2^k}$. This has been used in several works (e.g. here and here). For a recent study of this assumption, see here. In particular, this work points out that there is an easy "reduce modulo 2" attack on LPN over this ring that reduces the instance to an LPN instance over $\mathbb{F}_2$ and halves the amount of noise (since a random noise over $\mathbb{Z}_{2^k}$ is sent to 0 modulo 2 with probability half). This has to be taken into account when choosing parameters.
