Which model King Dome do you have?
If it's the 2200/3200 then here's what the manual says about switching vendors.
The King-DomeAIR is factory pre-set for DIRECTV® standard digital programming broadcast from the 101° W satellite. If you also receive your local channels from DIRECTV’s 119 satellite or if you subscribe to Dish Network® or Bell TV programming, YOU MUST RECONFIGURE THE ANTENNA to work with your satellite service. Doing this will allow the King-DomeAIR to lock on the correct satellites to receive your programming and also enable automatic satellite switching via the receiver’s remote control for multi-satellite service.
Looks like you'll have some configuration to do.