Strictly speaking, I would not call it a bug, because the output is correct. It is surely a shortcoming, which makes Reduce and FunctionDomain less useful, as you said. It very curious that the behaviour is so different going from a parameter 9 to a parameter 10. The command Solve does not suffer from this problem:

Reduce[x/10 \[Element] Integers && 0 <= x <= 10]
Solve[x/10 \[Element] Integers && 0 <= x <= 10]

The following

Reduce[Not[(Tan[x] + 1)/Tan[x] \[Element] Reals] && 
  0 <= x <= Pi, x, Reals]

gives False, which I find objectionable.

For some reason, Mathematica 11 can do these

Reduce[x \[Element] Integers && 0 <= x <= 1]
Reduce[x/9 \[Element] Integers && 0 <= x <= 9]

but not these:

Reduce[x/10 \[Element] Integers && 0 <= x <= 10]    
Reduce[x/\[Pi] \[Element] Integers && 0 <= x <= \[Pi]]