A two-party-consent state requires both people to consent to being recorded. So even if you (tacitly) agree to being recorded as a condition of your employment, if the person on the other end of the conversation doesn't then it's an illegal recording. That's why it probably wouldn't be an issue in one of those states.
But in a one party state, the other person on the recording doesn't have to consent as long as you do. So as long as you know your conversation is being recorded (again, hypothetically as a condition of employment) the other party (probably) doesn't have any recourse should your employer use a third-party to monitor it.