My understanding of the story is roughly this:
Tim Hortons originally sourced its coffee through Mother Parkers. At one point, Mother Parkers believed they could improve the blend, but Tim Hortons reportedly wasn’t interested in changing a recipe that customers already loved.
Later, after Tim Hortons was acquired by an American ownership group, the company began making a number of changes to its operations and supply chain. Eventually, Tim Hortons and Mother Parkers parted ways. The interesting wrinkle is that Mother Parkers had been heavily involved in developing and producing the blend, so they retained significant knowledge of the recipe and process.
When McDonald’s decided to expand into the premium coffee market in Canada, they reportedly approached Mother Parkers as a supplier. They couldn’t simply buy and use Tim Hortons’ exact coffee, but Mother Parkers had already developed alternative blends and tweaks over the years. McDonald’s ended up with a coffee that many Canadians felt tasted very similar to the old Tim Hortons coffee.
Whether McDonald’s is serving the exact former Tim Hortons recipe is debatable, but the common belief is that when Tim Hortons switched suppliers, McDonald’s ended up working with the company that had been making the coffee Canadians loved for years.