That's how it was with the LMAs we were involved with. But we always had two people who were employees of the owner, with one having to be management. The rest of the staff were employees of the LMA. At one point, our 2 FMs had separate owners, both LMAed to the same operator, so we had 4 people employed by the 2 owners, the rest by the LMA.
We never mentioned anything about LMAs on the air.
LMAs don't have to be mentioned on-air or passed by the FCC for approval. The documents do have to be in the station's public file.
The station licensee remains fully responsible for FCC compliance, as if they were actually running the station. This includes maintaining a "meaningful staff presence" at the stations main studio, responsibility for political content, verbage that gets "out of hand", sponsor identification and technical compliance. In practice, reality is usually much different.
There are several LMAs that I'm involved with, or am familiar with at arms-reach. In one case, the licensee owns the station's tower, which is also the home to two other stations. They provide full engineering for the site and LMA'd transmitter, with user access only to the audio processing and on/off control of the transmitter. Representing one of the tenants, I have full control of our transmitters, with access to the site owner's engineers as backup.
In another case, the licensee generally expect me (as a representative of the LMA) to handle maintenance, though they also have an available engineer and monitor the station's EAS system. As far as I can tell, they pay no attention to content and I can only assume they keep the public file in order.
In the other cases, I maintain full control of the stations' tower sites, even to the point that I have the only keys to the transmitter buildings. That certainly works for me, though I can see some FCC conflicts over positive control of the transmitter. Unfortunately, the licensee feels it's our baby and I get nowhere, trying to give them access. We're covered by a paper trail in that regard.
It can be a strange business!