You are basically correct, but the shorter answer is: it's complicated! Here's what Russell says in his more lucid moments:
I shall then briefly sketch the nature of that fundamental science which I believe to be the true metaphysic, in which mind and matter alike are seen to be constructed out of a neutral stuff, whose causal laws have no such duality as that of psychology, but form the basis upon which both physics and psychology are built. (The Analysis of Mind, pages 287-288)
It will be seen that the view which I am advocating is..."neutral monism". It is monism in the sense that it regards the world as composed of only one kind of stuff, namely events; but it is pluralism in the sense that it admits the existence of a great multiplicity of events, each minimal event being a logically self-subsistent entity. (An Outline of Philosophy page 293)
To show that the traditional separation between physics and psychology, mind and matter, is not metaphysically defensible, will be one of the purposes of this work; but the two will be brought together, not by subordinating either to the other, but by displaying each as a logical structure composed of what, following Dr H. M. Sheffer, we shall call "neutral stuff." (The Analysis of Matter, page 10)
However, a lot hinges on what you mean by "neutral." Russell holds that, although matter and mind are equally constructions of events (matter, the constructions of events obeying physical laws; mind, the constructions of events obeying psychological laws), some events (images) only obey psychological laws and all unexperienced events only obey physical laws:
...the American realists are partly right, though not wholly, in considering that mind and matter are composed of neutral-stuff which, in isolation, is neither mental nor physical. I would admit this view as regards sensations...But I should say that images belong only to the mental world, while those occurrences (if any) which do not form part of any "experience" belong only to the physical world. (The Analysis of Mind, page 25)
So to nitpick: while all events are not intrinsically either mental or physical, some events are such that they only are part of physical series of events, and others are only ever part of mental ones.