All neuromodulators (dopamine, serotonin, acetylcholine, histamine, and norepinephrine) act only on metabotropic receptors?
Not all neuromodulators act only on metabotropic receptors. However, you are correct to observe that this is a general rule of thumb.

Of the substances you have listed:


Acetylcholine is not primarily a neuromodulator, but rather a "normal" neurotransmitter. As such it acts on both ionotropic and metabotropic receptors.
Serotonin - the one exception among the neuromodulators you have listed - acts on numerous classes of metabotropic receptors, but also on the 5-HT3 receptor, which is ionotropic.
All other neuromodulators you have listed act on metabotropic receptors only.


This tendency of neuromodulation to be metabotropically mediated is possibly a consequence of the nature of the neuronal function itself. Neuromodulatory systems do not per se relay information, but change how other information relays work. As such there is no need for the most rapid, temporal, coding (best achieved via the more rapid ionotropic signal transduction), and a slower coding may even be more efficient.