Probably because the organization is Russian, and Mikhail is Russian so he should know their capabilities and strengths much better than Asami or Feilong's organizations are able to.
Also Mikhail is technically the one who started all this mess by stealing the goods. He was good and got away with it, but his actions has caused trouble for many parties who have nothing to do with it. Fei is probably thinking that it's only fair that he is responsible for crushing them.
Finally regarding Feilong's power. If we're comparing a Hong Kong syndicate to the Russian Mafia I don't think he's actually that powerful. Feilong's organization dealing with the Rebels on their own is pretty much impossible, they are more powerful than Baishe that's for sure.
If we compare forces, then Baishe is not inferior to either Asami or Mikhail. The Feilong Syndicate is influential in China and throughout Asia. Most likely the forces of Baishe and the Russian mafia are about equal. From a financial point of view, Asami is exactly inferior, but has her own strengths.
It is difficult to judge the reasons for the appeal of Feilong to Mikhail. He definitely needed information about the rebels, which Baishe did not own. And it was needed quickly. And also need to quickly eliminate the threat. Perhaps he does not want to bathe his people in the blood and put the organization at risk.
Feilong already realized that he was dealing with well-trained professionals (military?). Baishe probably has some killers, guards, etc. But most people hardly have the necessary training.
The quickest and bloodless course of action is to make a deal with Mikhail.
Ok, Fei wanted to protect Asami, I get that. And he was annoyed that rebels are acting on his teritorry, that is fine as well. But if he already decided to push away Asami from the whole deal and face the rebels, then why did he go directly to Mik instead of trying to deal with them on his own.
Though it makes sense that Fei would seek a partner to bring rebels down because it would be easier that way, Fei does not offer collaboration but asks Mik straightforward to do that alone? Fei is a powerful leader so it feels a bit off that he just wanted to order and pay someone to take care of it. Mik asked him - why me, and Fei evades to answer. So yeah, why Mik? ...aside from the fact that Fei guessed he would be easy to persuade.