Concurrent crises do not require a formal alliance

Do Russia, China, and Iran need to be coordinating in order to exploit simultaneous crises?

No; each can exploit the distraction created by the others, and formal coordination could create political risks if it were exposed.

Opportunism differs from an organized multi-state strategy. A government can observe that another crisis is absorbing American attention and decide independently that it has more room to act. Formal coordination is unnecessary for several pressures to arrive at once. Proven cooperation could also create problems for the participating states if the Americans detected it.