Can Actions Be Played on 1 base and "jump" to affect play on other bases?
An Ornate Dome on base B only prevents players from playing cards on base B (i.e. playing cards with "play on a base" on base B). I don't understand the scenario you are presenting in your question, but it doesn't seem to include anything affected by an Ornate Dome on base B. Specifically, Hidden Ninja is not played on a base, so it's not affected by Ornate Dome.