If the chord used a sharp or flat symbol before transposition, it will try to use the same after transposing the chord. If there was no sharp or flat symbol, Stage Traxx will currently prefer a flat modifier (my personal preference). But I just discovered that I left a TODO mark in the code to make this configurable. Completely forgot about that. I will add a configuration option in the next feature release.
Before I forget it: Stage Traxx does not know about the key a song is in. So when you say you transpose from C to E, this is just 4 semitones up for Stage Traxx. Therefore it will never choose the correct flat or sharp symbol for the destination key but the one defined in settings.