Oh dear. I'm sure someone else will come in to confirm but I'm pretty sure that a male still has sperm for a while after being neutered, it takes a few weeks for it to be totally gone. I do know that you're not supposed to have them together for the first few weeks until the hormones dissipate for behavioural reasons.
If your other male is 6 months, he's fully sexually matured, and can definitely reproduce. I would start asking some tough questions of your vet, if a) he's showing that kind of uncertainty over a rabbit neuter, which is about the same level of difficulty as a cat neuter (I.e. One of the simplest surgeries a vet will ever do) and the fact that b) he'd seen your male to assess for surgery and also had your female booked for a spay and didn't tell you to keep them separated?? Or warn you that the one that is neutered won't be immediately sterile????
That doesn't sound like a vet familiar with rabbits or like a vet that will give you good advice and client education.
Remember that the typical vet is ONLY educated to treat cats and dogs. Only a livestock or exotics vet has the education to treat more than that, and even then a practice that has an exotics vet hardly ever sees rabbits. The House Rabbit Society has an excellent page on the kinds of questions you can ask a vet to make sure they are both qualified and experienced enough to treat rabbits. You will often hear that spay and neuter surgeries are much riskier for rabbits—this has not been found to be true for vets that deal with rabbits on a regular basis, and their success rates are on par with those of cats and dogs, with the most fatalities occurring due to complications from anaesthesia, less than 1%. This is roughly similar to the surgery risk in humans, btw. Anaesthesia is always risky to an extent, but for a surgeon that knows what they're doing, rabbits are not any more at risk.