The first amendment does apply to your employer in that he can't muzzle you, or have you beaten up from speaking out. The worst your employer can do is fire you, which happens often, and that's fine.
In fact my employer can muzzle me. I've signed various documents over the years that prevent my from speaking about my employer (or past employers) in various ways.
And the fact that my employer can't have me beaten up has nothing to do with the 1st amendment. That would be assault no matter what their motivation.
The fact that your employer can't have you beaten up is because assault is illegal, not because of your first amendment rights. The first amendment protects you from being thrown in jail by the government for your speech.
