Hmmm, you are in trouble as the manufacture that made this chainsaw has been out of business for a long time. It is not the current McCulloch manufacture that brought the namesake which doe not support the older equipment.
It sounds like you have an air leak which probably is a crankshaft seal.
As for the McCulloch used both Walbro and Zama carburetors but I have yet to see one with a Tillotson. Pull the carburetor clean the exterior and look for the carburetor model numbers. The Walbro should the WT series and the Zama the C1U-M series. The first ones in the 80's where Zama that looks fairly strange then in the early 90's they switch to more familiar Walbro and Zama designs. Kits are still available for these but I need carb info to determine which kit you will need.
I had retire both my McCulloch Mac Cat and Wild Cat saws due oil pump failures but I still get McCulloch saws that just need fuel lines and carburetor work. I did a Mac 3516 last week.
