I own both a Miracle Mate & a Tri-Star......
Yes, you can use Tri-Star bags in a Miracle Mate. And, it certainly saves some money from being able to buy generic Tri-Star bags for about half the cost of the Miracle Mate bags. But, you will need to save the cardboard top from one of the Miracle Mate bags to put on top of the Tri-Star bag, otherwise it won't form a proper seal against the lid to create suction.
So, just be sure to buy a small pack of Miracle Mate bags first, & when you go to throw the bag out, cut off & save the lid off a couple & you're all set!
Rob