Trotsky's success with the Red Army wasn't as a general as such, he wasn't directing the battles for example. It was more a question of organsiation, getting the Red Army up to a standard where it could pose a threat to the Whites. The initial phases of the civil war had been fought on a relatively small scale and that could be carried by the militias and relatively small units like the Latvian Riflemen. As the conflict continued and the Whites got organised, the Bolsheviks needed to put together a larger force. That meant conscription, marshalling their forces and so forth. I forget whether it was Mawdsley or Lincoln who made the argument that the Bolsheviks actually had a really good position to win the civil war despite being surrounded by enemies, for example they had a large chunk of the population, controlled key transport hubs and even had a lot of the industrial base. But without someone to actually put all that together, the Reds would have been finished.

Trotsky's prior political work gave him some background in organising under pressure and with mixed resources. His skill and understanding of the use of propaganda etc. probably helped contribute to Red Army morale too (though he wasn't alone in this area). The armoured trains used during the civil war often had an attached Agitprop (agitation and propaganda) unit for this purpose.

Trotsky's support for former Tsarist officers makes sense in light of his not taking a field command role. He was willing to acknowledge his own (and his fellow Bolsheviks) lack of qualification (and also noting that elected officers were not a great idea) and hence left field command to the 'experts' essentially.

Makhno's forces I don't know much about. Their importance as far as I understood it had a lot to do with position and timing - the Bolsheviks were able to turn Makhno effectively against Denikin at a time when the Whites were already struggling with supply lines, and essentially turned the area the Whites were operating in hostile. Makhno's subsequent hostilities against the Reds is by association significant in that it prolonged conflict in that particular theatre of the civil war.