Does Containment Priest exile one's own creature?
does casting this creature mean that Containment Priest's controller would also have to exile all noncasted nontoken creatures?

Yes, when it comes to creatures entering the battlefield after Containment Priest. It does not mean you have to exile all existing non-token creatures.
Creatures entering simultaneously (including the Priest itself if it isn't cast) won't be affected, as is reflected by the rulings under the card in Gatherer:


If Containment Priest enters the battlefield without being cast, its ability won’t exile itself.

If Containment Priest enters the battlefield at the same time as other creatures, its ability won’t affect those creatures.