In addition to Gaelbert's comments, it would depend on how much General Tullius trusts Baalgruuf. Is Tullius comfortable enough to launch an attack on Eastmarch, knowing that his flank/rear is held by a neutral Whiterun at the very defensible Valtheim Towers?
Given Tullius' opinion and understanding of Skyrim and Nordic culture in general, he probably trusts them as far as he can throw them.
Not speaking as devil's advocate here, while I agree with the worst case, I'm going to dispute the best.
I wasn't aware that the Empire had immigration policies and passport/visa requirements, so at best, you're an innocent bystander who was in the wrong place at the wrong time.
Given the world's generally low regard for life, they're not going to shed any tears if an innocent person is executed, as you've said.