Hi, just want to offer a data point with this offer.
I had a "spend $400 get $40" in rewards offer and the free Target Circle 360 membership offer this week. I completed the $400/$40 offer today on two $200 DGCs and that also triggered my Target Circle 360 offer since I spent $199+. My Circle app said the year membership was available, BUT I needed to accept the 360 membership after making the purchase for it to activate to the actual membership.
It does not activate a membership automatically. I think it said the offer of the free membership expired in 35 days or something to that effect. If you do click accept, it takes you through several terms and conditions you need to approve before finally activating. I do need a 360 this year for various reasons, so I accepted the free membership.