That behaviour would be expected. On a standard tube screamer, both input and output buffers are always in the signal path regardless if the effect is engaged or not.
If you look at this
schematic you can see that Q1 and Q2 are connected to the Flipflop circuit. The idea here is that Q1 turns off and Q2 turns on when the effect is engaged. Then the opposite when the effect is bypassed.
But...as you can see...both buffers are always present. The switching happens after the input but before the output. Sometimes we are all so hardcore on going True Bypass that we ignore the very real benefits of buffers!...In this case, having a circuit that will sound consistent regardless of where you put it in your chain, regardless of what comes before/after it.