Season Series
https://www.espn.com/mlb/standings/grid
Det-KC
KC 7 Det 6
Det-Minn
Minn 7 Det 6
Det-Sea
Det 5 Sea 1
Sea-KC
Sea 3 KC 3
Sea-Minn
Minn 5 Sea 2
KC-Minn
Minn 7 KC 6
Here is why I think the Tigers would win the tiebreaker with KC as long as it was a 3-way tie involving Seattle. The Tigers head to head to head against KC and Seattle is 11-8, KC's is 10-9, and Seattle's is 4-8.
How about a 3-way tie with Minnesota and Seattle? The Tigers' head to head to head against Minnesota and Seattle is 11-8, Minnesota's is 12-8, and Seattle's is 3-8. So the Tigers would still lose a tiebreaker to Minnesota, even if it involves Seattle too.
How about a 4-way tie with Detroit, KC, Minnesota and Seattle, with two teams making it? The Tigers' head to head to head to head against KC, Minnesota and Seattle is 17-15, KC's is 16-16, Minnesota's is 19-14, Seattle's is 6-13. So the Twins and Tigers would make it.