(Some editions of the libretto omit this line.)

It means pledged to secrecy as in a fraternal order. Brewer (54) explains the term “to tile a lodge” as follows:

“In Freemasonry, is to close and guard the doors to prevent anyone uninitiated from entering.” Barker (26) says that in former times Freemasons’ secret meetings were guarded by a door-keeper called a “tiler.” Gilbert and Sullivan, incidentally, were both Masons (142, 163, 275).

we’re all tiled, here.
Act I