Theo is a beta. The Seigfried family doesn't have omega servants. And I highly doubt a family would allow an alpha son to be a servant either.
He couldn't be with the twins. They have to have a heat to be able to "accept" the alpha. It's why the omegas use the drugs to induce the heat symptoms outside of the normal cycle. Their bodies can't handle it otherwise.
Has it been stated explicitly? No, you're right. But what was stated in both Remnant and Pendulum is that the only thing omegas are allowed to do in the Seigfried household is have babies. Kai was supposed to be added to the breeding group once his heat came. Baron scoffed at Daato thinking he'd be a servant.
Alphas are rare, even human ones. They're supposed to be the best and the brightest. You really think any family would let their alpha son be a servant?
Betas are the vast majority of the population. The exceptionally overwhelming likelihood is that Theo is one.
One of the twins is going to get with theo