It should show an A# yes. (or Bb)
The only trumpets/cornets etc which will show a C is the C-trumpet/cornet etc.
The rest is so called "transposed" instruments in The keys of A Bb D E Eb F or G
It is possible to figure out which key an instrument is built in by
finding out were the C is on the actual instrument and check the tuner which will show the (transposed) note
which will be the key. Easiest way to find the C is to play C-D-G-C (if one can find them....)