The affidavit refers to Bieber as "Victim 3" or "J.B." who was the "ultimate target."
McDonald told CNN that J.B. refers to Justin Bieber.
A representative for 18-year-old Bieber said, "We take every precaution to protect and ensure the safety of Justin and his fans."
Bieber rose to fame in 2009 with his hit single "One Time." He was named Artist of the Year at the American Music Awards in both 2010 and 2012.
Martin and Staake met while inmates in the Southern New Mexico Correctional Facility after Martin was transferred there from a Florida prison in April, the affidavit said. Staake was released and put on probation on October 22. McDonald didn't know why Martin was in a Florida prison, he said.
"When asked how he was able to convince Mr. Staake to participate, Mr. Martin stated he (Mr. Martin) was a very good manipulator," the court document said. Martin also promised money and a Vermont farm as a hideout, the affidavit said.
Martin remains under investigation and is in fact named in the affidavit as a conspirator in the Vermont plot. The affidavit was filed in Dona Ana County for seeking an arrest warrant against Staake.
But Martin hasn't been formally charged in any of the plots, McDonald said.
"For us, there's no rush (for charges) as far as Martin is concerned because he's serving life sentences anyway," McDonald said.
Media across the world have been calling McDonald.
"It's been freaking crazy," he said. "But the good thing is we nipped this thing in the bud and we caught it before anyone was hurt.
"We're definitely thankful -- we owe it to the guard at the correctional facility who caught these phone calls and got on it right away. That's how we were able to catch these guys," McDonald said.